11x1 t05 01 permutations i (2011)

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The Basic Counting Principle

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Page 1: 11X1 T05 01 permutations I (2011)

The Basic Counting Principle

Page 2: 11X1 T05 01 permutations I (2011)

The Basic Counting PrincipleIf one event can happen in m different ways and after this another event can happen in n different ways, then the two events can occur in mn different ways.

Page 3: 11X1 T05 01 permutations I (2011)

The Basic Counting PrincipleIf one event can happen in m different ways and after this another event can happen in n different ways, then the two events can occur in mn different ways.

e.g. 3 dice are rolled

Page 4: 11X1 T05 01 permutations I (2011)

The Basic Counting PrincipleIf one event can happen in m different ways and after this another event can happen in n different ways, then the two events can occur in mn different ways.

e.g. 3 dice are rolled(i) How many ways can the three dice fall?

Page 5: 11X1 T05 01 permutations I (2011)

The Basic Counting PrincipleIf one event can happen in m different ways and after this another event can happen in n different ways, then the two events can occur in mn different ways.

e.g. 3 dice are rolled(i) How many ways can the three dice fall?

666 Ways

Page 6: 11X1 T05 01 permutations I (2011)

The Basic Counting PrincipleIf one event can happen in m different ways and after this another event can happen in n different ways, then the two events can occur in mn different ways.

e.g. 3 dice are rolled(i) How many ways can the three dice fall?

666 Ways

iespossibilit6has die1st the

Page 7: 11X1 T05 01 permutations I (2011)

The Basic Counting PrincipleIf one event can happen in m different ways and after this another event can happen in n different ways, then the two events can occur in mn different ways.

e.g. 3 dice are rolled(i) How many ways can the three dice fall?

666 Ways

iespossibilit6has die1st theiespossibilit6hasdie2ndthe

Page 8: 11X1 T05 01 permutations I (2011)

The Basic Counting PrincipleIf one event can happen in m different ways and after this another event can happen in n different ways, then the two events can occur in mn different ways.

e.g. 3 dice are rolled(i) How many ways can the three dice fall?

666 Ways

iespossibilit6has die1st theiespossibilit6hasdie2ndthe

iespossibilit6has die3rdthe

Page 9: 11X1 T05 01 permutations I (2011)

The Basic Counting PrincipleIf one event can happen in m different ways and after this another event can happen in n different ways, then the two events can occur in mn different ways.

e.g. 3 dice are rolled(i) How many ways can the three dice fall?

666 Ways

iespossibilit6has die1st theiespossibilit6hasdie2ndthe

iespossibilit6has die3rdthe612

Page 10: 11X1 T05 01 permutations I (2011)

(ii) How many ways can all three dice show the same number?

Page 11: 11X1 T05 01 permutations I (2011)

(ii) How many ways can all three dice show the same number?

116 Ways

Page 12: 11X1 T05 01 permutations I (2011)

(ii) How many ways can all three dice show the same number?

116 Ways

iespossibilit6has die1st the

Page 13: 11X1 T05 01 permutations I (2011)

(ii) How many ways can all three dice show the same number?

116 Ways

iespossibilit6has die1st theypossibilit1only has nowdie2ndthe

Page 14: 11X1 T05 01 permutations I (2011)

(ii) How many ways can all three dice show the same number?

116 Ways

iespossibilit6has die1st theypossibilit1only has nowdie2ndthe

ypossibilit1only has nowdie3rdthe

Page 15: 11X1 T05 01 permutations I (2011)

(ii) How many ways can all three dice show the same number?

116 Ways

iespossibilit6has die1st theypossibilit1only has nowdie2ndthe

ypossibilit1only has nowdie3rdthe6

Page 16: 11X1 T05 01 permutations I (2011)

(ii) How many ways can all three dice show the same number?

116 Ways

iespossibilit6has die1st theypossibilit1only has nowdie2ndthe

ypossibilit1only has nowdie3rdthe6

(iii) What is the probability that all three dice show the same number?

Page 17: 11X1 T05 01 permutations I (2011)

(ii) How many ways can all three dice show the same number?

116 Ways

iespossibilit6has die1st theypossibilit1only has nowdie2ndthe

ypossibilit1only has nowdie3rdthe6

(iii) What is the probability that all three dice show the same number?

2166same the3 all P

Page 18: 11X1 T05 01 permutations I (2011)

(ii) How many ways can all three dice show the same number?

116 Ways

iespossibilit6has die1st theypossibilit1only has nowdie2ndthe

ypossibilit1only has nowdie3rdthe6

(iii) What is the probability that all three dice show the same number?

2166same the3 all P

361

Page 19: 11X1 T05 01 permutations I (2011)

Mice are placed in the centre of a maze which has five exits.

Each mouse is equally likely to leave the maze through any of the five exits. Thus, the probability of any given mouse leaving by a particular exit is

Four mice, A, B, C and D are put into the maze and behave independently.

(i) What is the probability that A, B, C and D all come out the same exit?

51

1996 Extension 1 HSC Q5c)

Page 20: 11X1 T05 01 permutations I (2011)

Mice are placed in the centre of a maze which has five exits.

Each mouse is equally likely to leave the maze through any of the five exits. Thus, the probability of any given mouse leaving by a particular exit is

Four mice, A, B, C and D are put into the maze and behave independently.

(i) What is the probability that A, B, C and D all come out the same exit?

51

1996 Extension 1 HSC Q5c)

51

51

511exit same theuse all P

Page 21: 11X1 T05 01 permutations I (2011)

Mice are placed in the centre of a maze which has five exits.

Each mouse is equally likely to leave the maze through any of the five exits. Thus, the probability of any given mouse leaving by a particular exit is

Four mice, A, B, C and D are put into the maze and behave independently.

(i) What is the probability that A, B, C and D all come out the same exit?

51

1996 Extension 1 HSC Q5c)

51

51

511exit same theuse all P

1door any through gocan mouseFirst P

Page 22: 11X1 T05 01 permutations I (2011)

Mice are placed in the centre of a maze which has five exits.

Each mouse is equally likely to leave the maze through any of the five exits. Thus, the probability of any given mouse leaving by a particular exit is

Four mice, A, B, C and D are put into the maze and behave independently.

(i) What is the probability that A, B, C and D all come out the same exit?

51

1996 Extension 1 HSC Q5c)

51

51

511exit same theuse all P

1door any through gocan mouseFirst P

51door samethrough

gomust miceOther

P

Page 23: 11X1 T05 01 permutations I (2011)

Mice are placed in the centre of a maze which has five exits.

Each mouse is equally likely to leave the maze through any of the five exits. Thus, the probability of any given mouse leaving by a particular exit is

Four mice, A, B, C and D are put into the maze and behave independently.

(i) What is the probability that A, B, C and D all come out the same exit?

51

1996 Extension 1 HSC Q5c)

51

51

511exit same theuse all P

1door any through gocan mouseFirst P

51door samethrough

gomust miceOther

P

1251

Page 24: 11X1 T05 01 permutations I (2011)

(ii) What is the probability that A, B and C come out the same exit and D comes out a different exit?

Page 25: 11X1 T05 01 permutations I (2011)

(ii) What is the probability that A, B and C come out the same exit and D comes out a different exit?

51

51

541exitdifferent uses exit, same use DABCP

Page 26: 11X1 T05 01 permutations I (2011)

(ii) What is the probability that A, B and C come out the same exit and D comes out a different exit?

51

51

541exitdifferent uses exit, same use DABCP

1door any through gocan D P

Page 27: 11X1 T05 01 permutations I (2011)

(ii) What is the probability that A, B and C come out the same exit and D comes out a different exit?

51

51

541exitdifferent uses exit, same use DABCP

1door any through gocan D P

54

choosetodoors4hasmouseNext

P

Page 28: 11X1 T05 01 permutations I (2011)

(ii) What is the probability that A, B and C come out the same exit and D comes out a different exit?

51

51

541exitdifferent uses exit, same use DABCP

1door any through gocan D P

54

choosetodoors4hasmouseNext

P

51door samethrough

gomust miceOther

P

Page 29: 11X1 T05 01 permutations I (2011)

(ii) What is the probability that A, B and C come out the same exit and D comes out a different exit?

51

51

541exitdifferent uses exit, same use DABCP

1door any through gocan D P

54

choosetodoors4hasmouseNext

P

1254

51door samethrough

gomust miceOther

P

Page 30: 11X1 T05 01 permutations I (2011)

(iii) What is the probability that any of the four mice come out the same exit and the other comes out a different exit?

Page 31: 11X1 T05 01 permutations I (2011)

(iii) What is the probability that any of the four mice come out the same exit and the other comes out a different exit?

125

4exitdifferent uses DP

Page 32: 11X1 T05 01 permutations I (2011)

(iii) What is the probability that any of the four mice come out the same exit and the other comes out a different exit?

125

4exitdifferent uses DP

125

4exitdifferent uses AP

Page 33: 11X1 T05 01 permutations I (2011)

(iii) What is the probability that any of the four mice come out the same exit and the other comes out a different exit?

125

4exitdifferent uses DP

125

4exitdifferent uses AP

125

4exitdifferent uses BP

Page 34: 11X1 T05 01 permutations I (2011)

(iii) What is the probability that any of the four mice come out the same exit and the other comes out a different exit?

125

4exitdifferent uses DP

125

4exitdifferent uses AP

125

4exitdifferent uses BP

125

4exitdifferent uses CP

Page 35: 11X1 T05 01 permutations I (2011)

(iii) What is the probability that any of the four mice come out the same exit and the other comes out a different exit?

125

4exitdifferent uses DP

125

4exitdifferent uses AP

125

4exitdifferent uses BP

125

4exitdifferent uses CP

125

44exitdifferent uses mouseany P

Page 36: 11X1 T05 01 permutations I (2011)

(iii) What is the probability that any of the four mice come out the same exit and the other comes out a different exit?

125

4exitdifferent uses DP

125

4exitdifferent uses AP

125

4exitdifferent uses BP

125

4exitdifferent uses CP

125

44exitdifferent uses mouseany P

12516

Page 37: 11X1 T05 01 permutations I (2011)

(iv) What is the probability that no more than two mice come out the same exit?

Page 38: 11X1 T05 01 permutations I (2011)

(iv) What is the probability that no more than two mice come out the same exit?

sameuse3sameall1exitsameuse2 than moreno PPP

Page 39: 11X1 T05 01 permutations I (2011)

(iv) What is the probability that no more than two mice come out the same exit?

sameuse3sameall1exitsameuse2 than moreno PPP

12516

12511

Page 40: 11X1 T05 01 permutations I (2011)

(iv) What is the probability that no more than two mice come out the same exit?

sameuse3sameall1exitsameuse2 than moreno PPP

12516

12511

125108

Page 41: 11X1 T05 01 permutations I (2011)

Permutations

Page 42: 11X1 T05 01 permutations I (2011)

PermutationsA permutation is an ordered set of objects

Page 43: 11X1 T05 01 permutations I (2011)

PermutationsA permutation is an ordered set of objects

Case 1: Ordered Sets of n Different Objects, from a Set of n Such Objects

Page 44: 11X1 T05 01 permutations I (2011)

PermutationsA permutation is an ordered set of objects

Case 1: Ordered Sets of n Different Objects, from a Set of n Such Objects

(i.e. use all of the objects)

Page 45: 11X1 T05 01 permutations I (2011)

PermutationsA permutation is an ordered set of objects

Case 1: Ordered Sets of n Different Objects, from a Set of n Such Objects

If we arrange n different objects in a line, the number of ways we could arrange them are;

(i.e. use all of the objects)

Page 46: 11X1 T05 01 permutations I (2011)

PermutationsA permutation is an ordered set of objects

Case 1: Ordered Sets of n Different Objects, from a Set of n Such Objects

If we arrange n different objects in a line, the number of ways we could arrange them are;

ntsArrangemen ofNumber 1object for

iespossibilit

(i.e. use all of the objects)

Page 47: 11X1 T05 01 permutations I (2011)

PermutationsA permutation is an ordered set of objects

Case 1: Ordered Sets of n Different Objects, from a Set of n Such Objects

If we arrange n different objects in a line, the number of ways we could arrange them are;

ntsArrangemen ofNumber 1object for

iespossibilit

(i.e. use all of the objects)

1 n

2object for iespossibilit

Page 48: 11X1 T05 01 permutations I (2011)

PermutationsA permutation is an ordered set of objects

Case 1: Ordered Sets of n Different Objects, from a Set of n Such Objects

If we arrange n different objects in a line, the number of ways we could arrange them are;

ntsArrangemen ofNumber 1object for

iespossibilit

(i.e. use all of the objects)

1 n 2 n

2object for iespossibilit

3object for iespossibilit

Page 49: 11X1 T05 01 permutations I (2011)

PermutationsA permutation is an ordered set of objects

Case 1: Ordered Sets of n Different Objects, from a Set of n Such Objects

If we arrange n different objects in a line, the number of ways we could arrange them are;

ntsArrangemen ofNumber 1object for

iespossibilit

(i.e. use all of the objects)

1 n 2 n 1

2object for iespossibilit

3object for iespossibilit

objectlast for iespossibilit

Page 50: 11X1 T05 01 permutations I (2011)

PermutationsA permutation is an ordered set of objects

Case 1: Ordered Sets of n Different Objects, from a Set of n Such Objects

If we arrange n different objects in a line, the number of ways we could arrange them are;

ntsArrangemen ofNumber 1object for

iespossibilit

!n

(i.e. use all of the objects)

1 n 2 n 1

2object for iespossibilit

3object for iespossibilit

objectlast for iespossibilit

Page 51: 11X1 T05 01 permutations I (2011)

e.g. In how many ways can 5 boys and 4 girls be arranged in a line if;

(i) there are no restrictions?

Page 52: 11X1 T05 01 permutations I (2011)

e.g. In how many ways can 5 boys and 4 girls be arranged in a line if;

(i) there are no restrictions?

!9tsArrangemen

Page 53: 11X1 T05 01 permutations I (2011)

e.g. In how many ways can 5 boys and 4 girls be arranged in a line if;

(i) there are no restrictions?

!9tsArrangemen With no restrictions, arrange 9 peoplegender does not matter

Page 54: 11X1 T05 01 permutations I (2011)

e.g. In how many ways can 5 boys and 4 girls be arranged in a line if;

(i) there are no restrictions?

!9tsArrangemen With no restrictions, arrange 9 peoplegender does not matter 362880

Page 55: 11X1 T05 01 permutations I (2011)

e.g. In how many ways can 5 boys and 4 girls be arranged in a line if;

(i) there are no restrictions?

!9tsArrangemen With no restrictions, arrange 9 peoplegender does not matter 362880

(ii) boys and girls alternate?

Page 56: 11X1 T05 01 permutations I (2011)

e.g. In how many ways can 5 boys and 4 girls be arranged in a line if;

(i) there are no restrictions?

!9tsArrangemen With no restrictions, arrange 9 peoplegender does not matter 362880

(ii) boys and girls alternate? (ALWAYS look after any restrictions first)

Page 57: 11X1 T05 01 permutations I (2011)

e.g. In how many ways can 5 boys and 4 girls be arranged in a line if;

(i) there are no restrictions?

!9tsArrangemen With no restrictions, arrange 9 peoplegender does not matter 362880

(ii) boys and girls alternate?

1tsArrangemen

boy a beMUSTperson first

(ALWAYS look after any restrictions first)

Page 58: 11X1 T05 01 permutations I (2011)

e.g. In how many ways can 5 boys and 4 girls be arranged in a line if;

(i) there are no restrictions?

!9tsArrangemen With no restrictions, arrange 9 peoplegender does not matter 362880

(ii) boys and girls alternate?

1tsArrangemen

boy a beMUSTperson first

(ALWAYS look after any restrictions first)

!5

boys thearrangingof waysofnumber

Page 59: 11X1 T05 01 permutations I (2011)

e.g. In how many ways can 5 boys and 4 girls be arranged in a line if;

(i) there are no restrictions?

!9tsArrangemen With no restrictions, arrange 9 peoplegender does not matter 362880

(ii) boys and girls alternate?

1tsArrangemen

boy a beMUSTperson first

(ALWAYS look after any restrictions first)

!5 !4

boys thearrangingof waysofnumber

girls thearrangingofwaysofnumber

Page 60: 11X1 T05 01 permutations I (2011)

e.g. In how many ways can 5 boys and 4 girls be arranged in a line if;

(i) there are no restrictions?

!9tsArrangemen With no restrictions, arrange 9 peoplegender does not matter 362880

(ii) boys and girls alternate?

1tsArrangemen

boy a beMUSTperson first

(ALWAYS look after any restrictions first)

!5 !4

boys thearrangingof waysofnumber

girls thearrangingofwaysofnumber

2880

Page 61: 11X1 T05 01 permutations I (2011)

(iii) What is the probability of the boys and girls alternating?

Page 62: 11X1 T05 01 permutations I (2011)

(iii) What is the probability of the boys and girls alternating?

362880

2880alternate girls & boys P

Page 63: 11X1 T05 01 permutations I (2011)

(iii) What is the probability of the boys and girls alternating?

362880

2880alternate girls & boys P

1261

Page 64: 11X1 T05 01 permutations I (2011)

(iii) What is the probability of the boys and girls alternating?

362880

2880alternate girls & boys P

1261

(iv) Two girls wish to be together?

Page 65: 11X1 T05 01 permutations I (2011)

(iii) What is the probability of the boys and girls alternating?

362880

2880alternate girls & boys P

1261

(iv) Two girls wish to be together?

!2tsArrangemen

arranged becan girlsthewaysofnumber the

Page 66: 11X1 T05 01 permutations I (2011)

(iii) What is the probability of the boys and girls alternating?

362880

2880alternate girls & boys P

1261

(iv) Two girls wish to be together?

!2tsArrangemen

arranged becan girlsthewaysofnumber the

!8 others 7 girls) (2objects 8 arranging

ofwaysofnumber

Page 67: 11X1 T05 01 permutations I (2011)

(iii) What is the probability of the boys and girls alternating?

362880

2880alternate girls & boys P

1261

(iv) Two girls wish to be together?

!2tsArrangemen

arranged becan girlsthewaysofnumber the

!8 others 7 girls) (2objects 8 arranging

ofwaysofnumber

80640

Page 68: 11X1 T05 01 permutations I (2011)

Case 2: Ordered Sets of k Different Objects, from a Set of n Such Objects (k < n)

Page 69: 11X1 T05 01 permutations I (2011)

Case 2: Ordered Sets of k Different Objects, from a Set of n Such Objects (k < n)

(i.e. use some of the objects)

Page 70: 11X1 T05 01 permutations I (2011)

Case 2: Ordered Sets of k Different Objects, from a Set of n Such Objects (k < n)

If we have n different objects in a line, but only want to arrange k of them, the number of ways we could arrange them are;

(i.e. use some of the objects)

Page 71: 11X1 T05 01 permutations I (2011)

Case 2: Ordered Sets of k Different Objects, from a Set of n Such Objects (k < n)

If we have n different objects in a line, but only want to arrange k of them, the number of ways we could arrange them are;

ntsArrangemen ofNumber 1object for

iespossibilit

(i.e. use some of the objects)

Page 72: 11X1 T05 01 permutations I (2011)

Case 2: Ordered Sets of k Different Objects, from a Set of n Such Objects (k < n)

If we have n different objects in a line, but only want to arrange k of them, the number of ways we could arrange them are;

ntsArrangemen ofNumber 1object for

iespossibilit

(i.e. use some of the objects)

1 n

2object for iespossibilit

Page 73: 11X1 T05 01 permutations I (2011)

Case 2: Ordered Sets of k Different Objects, from a Set of n Such Objects (k < n)

If we have n different objects in a line, but only want to arrange k of them, the number of ways we could arrange them are;

ntsArrangemen ofNumber 1object for

iespossibilit

(i.e. use some of the objects)

1 n 2 n

2object for iespossibilit

3object for iespossibilit

Page 74: 11X1 T05 01 permutations I (2011)

Case 2: Ordered Sets of k Different Objects, from a Set of n Such Objects (k < n)

If we have n different objects in a line, but only want to arrange k of them, the number of ways we could arrange them are;

ntsArrangemen ofNumber 1object for

iespossibilit

(i.e. use some of the objects)

1 n 2 n 1 kn

2object for iespossibilit

3object for iespossibilit

kobject for iespossibilit

Page 75: 11X1 T05 01 permutations I (2011)

Case 2: Ordered Sets of k Different Objects, from a Set of n Such Objects (k < n)

If we have n different objects in a line, but only want to arrange k of them, the number of ways we could arrange them are;

ntsArrangemen ofNumber 1object for

iespossibilit

1231

1231121

knknknknknnnn

(i.e. use some of the objects)

1 n 2 n 1 kn

2object for iespossibilit

3object for iespossibilit

kobject for iespossibilit

Page 76: 11X1 T05 01 permutations I (2011)

Case 2: Ordered Sets of k Different Objects, from a Set of n Such Objects (k < n)

If we have n different objects in a line, but only want to arrange k of them, the number of ways we could arrange them are;

ntsArrangemen ofNumber 1object for

iespossibilit

1231

1231121

knknknknknnnn

(i.e. use some of the objects)

1 n 2 n 1 kn

2object for iespossibilit

3object for iespossibilit

kobject for iespossibilit

!! kn

n

Page 77: 11X1 T05 01 permutations I (2011)

Case 2: Ordered Sets of k Different Objects, from a Set of n Such Objects (k < n)

If we have n different objects in a line, but only want to arrange k of them, the number of ways we could arrange them are;

ntsArrangemen ofNumber 1object for

iespossibilit

1231

1231121

knknknknknnnn

(i.e. use some of the objects)

1 n 2 n 1 kn

2object for iespossibilit

3object for iespossibilit

kobject for iespossibilit

!! kn

n

knP

Page 78: 11X1 T05 01 permutations I (2011)

e.g. (i) From the letters of the word PROBLEMS how many 5 letter words are possible if;

a) there are no restrictions?

Page 79: 11X1 T05 01 permutations I (2011)

e.g. (i) From the letters of the word PROBLEMS how many 5 letter words are possible if;

a) there are no restrictions?

58 Words P

Page 80: 11X1 T05 01 permutations I (2011)

e.g. (i) From the letters of the word PROBLEMS how many 5 letter words are possible if;

a) there are no restrictions?

58 Words P6720

Page 81: 11X1 T05 01 permutations I (2011)

e.g. (i) From the letters of the word PROBLEMS how many 5 letter words are possible if;

a) there are no restrictions?

58 Words P6720

b) they must begin with P?

Page 82: 11X1 T05 01 permutations I (2011)

e.g. (i) From the letters of the word PROBLEMS how many 5 letter words are possible if;

a) there are no restrictions?

58 Words P6720

b) they must begin with P?

1Words

first placed becan Pwaysofnumber the

Page 83: 11X1 T05 01 permutations I (2011)

e.g. (i) From the letters of the word PROBLEMS how many 5 letter words are possible if;

a) there are no restrictions?

58 Words P6720

b) they must begin with P?

1Words

first placed becan Pwaysofnumber the

47 P ROBLEMS

dsletter wor 4many howbecomesnowQuestion

Page 84: 11X1 T05 01 permutations I (2011)

e.g. (i) From the letters of the word PROBLEMS how many 5 letter words are possible if;

a) there are no restrictions?

58 Words P6720

b) they must begin with P?

1Words

first placed becan Pwaysofnumber the

47 P ROBLEMS

dsletter wor 4many howbecomesnowQuestion

840

Page 85: 11X1 T05 01 permutations I (2011)

c) P is included, but not at the beginning, and M is excluded?

Page 86: 11X1 T05 01 permutations I (2011)

c) P is included, but not at the beginning, and M is excluded?

4Words

in placed becan Ppositionsofnumber the

Page 87: 11X1 T05 01 permutations I (2011)

c) P is included, but not at the beginning, and M is excluded?

4Words

in placed becan Ppositionsofnumber the

46 P ROBLES

dsletter wor 4many howbecomesnowQuestion

Page 88: 11X1 T05 01 permutations I (2011)

c) P is included, but not at the beginning, and M is excluded?

4Words

in placed becan Ppositionsofnumber the

46 P ROBLES

dsletter wor 4many howbecomesnowQuestion

1440

Page 89: 11X1 T05 01 permutations I (2011)

c) P is included, but not at the beginning, and M is excluded?

4Words

in placed becan Ppositionsofnumber the

46 P ROBLES

dsletter wor 4many howbecomesnowQuestion

1440

(ii) Six people are in a boat with eight seats, for on each side.What is the probability that Bill and Ted are on the left side and Greg is on the right?

Page 90: 11X1 T05 01 permutations I (2011)

c) P is included, but not at the beginning, and M is excluded?

4Words

in placed becan Ppositionsofnumber the

46 P ROBLES

dsletter wor 4many howbecomesnowQuestion

1440

(ii) Six people are in a boat with eight seats, for on each side.What is the probability that Bill and Ted are on the left side and Greg is on the right?

68 ns)restrictio (no Ways P

Page 91: 11X1 T05 01 permutations I (2011)

c) P is included, but not at the beginning, and M is excluded?

4Words

in placed becan Ppositionsofnumber the

46 P ROBLES

dsletter wor 4many howbecomesnowQuestion

1440

(ii) Six people are in a boat with eight seats, for on each side.What is the probability that Bill and Ted are on the left side and Greg is on the right?

68 ns)restrictio (no Ways P20160

Page 92: 11X1 T05 01 permutations I (2011)

c) P is included, but not at the beginning, and M is excluded?

4Words

in placed becan Ppositionsofnumber the

46 P ROBLES

dsletter wor 4many howbecomesnowQuestion

1440

(ii) Six people are in a boat with eight seats, for on each side.What is the probability that Bill and Ted are on the left side and Greg is on the right?

68 ns)restrictio (no Ways P20160

24 ons)(restricti Ways P

gocan Ted & BillWays

Page 93: 11X1 T05 01 permutations I (2011)

c) P is included, but not at the beginning, and M is excluded?

4Words

in placed becan Ppositionsofnumber the

46 P ROBLES

dsletter wor 4many howbecomesnowQuestion

1440

(ii) Six people are in a boat with eight seats, for on each side.What is the probability that Bill and Ted are on the left side and Greg is on the right?

68 ns)restrictio (no Ways P20160

24 ons)(restricti Ways P

gocan Ted & BillWays

14P

gocan GregWays

Page 94: 11X1 T05 01 permutations I (2011)

c) P is included, but not at the beginning, and M is excluded?

4Words

in placed becan Ppositionsofnumber the

46 P ROBLES

dsletter wor 4many howbecomesnowQuestion

1440

(ii) Six people are in a boat with eight seats, for on each side.What is the probability that Bill and Ted are on the left side and Greg is on the right?

68 ns)restrictio (no Ways P20160

24 ons)(restricti Ways P

gocan Ted & BillWays

14P 3

5P

gocan GregWays

gocan peopleremainingWays

Page 95: 11X1 T05 01 permutations I (2011)

c) P is included, but not at the beginning, and M is excluded?

4Words

in placed becan Ppositionsofnumber the

46 P ROBLES

dsletter wor 4many howbecomesnowQuestion

1440

(ii) Six people are in a boat with eight seats, for on each side.What is the probability that Bill and Ted are on the left side and Greg is on the right?

68 ns)restrictio (no Ways P20160

24 ons)(restricti Ways P

gocan Ted & BillWays

14P 3

5P

gocan GregWays

gocan peopleremainingWays

2880

Page 96: 11X1 T05 01 permutations I (2011)

c) P is included, but not at the beginning, and M is excluded?

4Words

in placed becan Ppositionsofnumber the

46 P ROBLES

dsletter wor 4many howbecomesnowQuestion

1440

(ii) Six people are in a boat with eight seats, for on each side.What is the probability that Bill and Ted are on the left side and Greg is on the right?

68 ns)restrictio (no Ways P20160

24 ons)(restricti Ways P

gocan Ted & BillWays

14P 3

5P

gocan GregWays

gocan peopleremainingWays

2880

201602880rightG left, T&B P

Page 97: 11X1 T05 01 permutations I (2011)

c) P is included, but not at the beginning, and M is excluded?

4Words

in placed becan Ppositionsofnumber the

46 P ROBLES

dsletter wor 4many howbecomesnowQuestion

1440

(ii) Six people are in a boat with eight seats, for on each side.What is the probability that Bill and Ted are on the left side and Greg is on the right?

68 ns)restrictio (no Ways P20160

24 ons)(restricti Ways P

gocan Ted & BillWays

14P 3

5P

gocan GregWays

gocan peopleremainingWays

2880

201602880rightG left, T&B P

71

Page 98: 11X1 T05 01 permutations I (2011)

Sophia has five coloured blocks: one red, one blue, one green, one yellow and one white.

She stacks two, three, four or five blocks on top of one another to form a vertical tower.

2006 Extension 1 HSC Q3c)

Page 99: 11X1 T05 01 permutations I (2011)

Sophia has five coloured blocks: one red, one blue, one green, one yellow and one white.

She stacks two, three, four or five blocks on top of one another to form a vertical tower.

2006 Extension 1 HSC Q3c)

(i) How many different towers are there that she could form that are three blocks high?

Page 100: 11X1 T05 01 permutations I (2011)

Sophia has five coloured blocks: one red, one blue, one green, one yellow and one white.

She stacks two, three, four or five blocks on top of one another to form a vertical tower.

2006 Extension 1 HSC Q3c)

(i) How many different towers are there that she could form that are three blocks high?

35 Towers P

Page 101: 11X1 T05 01 permutations I (2011)

Sophia has five coloured blocks: one red, one blue, one green, one yellow and one white.

She stacks two, three, four or five blocks on top of one another to form a vertical tower.

2006 Extension 1 HSC Q3c)

(i) How many different towers are there that she could form that are three blocks high?

35 Towers P60

Page 102: 11X1 T05 01 permutations I (2011)

Sophia has five coloured blocks: one red, one blue, one green, one yellow and one white.

She stacks two, three, four or five blocks on top of one another to form a vertical tower.

2006 Extension 1 HSC Q3c)

(i) How many different towers are there that she could form that are three blocks high?

35 Towers P60

(ii) How many different towers can she form in total?

Page 103: 11X1 T05 01 permutations I (2011)

Sophia has five coloured blocks: one red, one blue, one green, one yellow and one white.

She stacks two, three, four or five blocks on top of one another to form a vertical tower.

2006 Extension 1 HSC Q3c)

(i) How many different towers are there that she could form that are three blocks high?

35 Towers P60

(ii) How many different towers can she form in total?

25 Towersblock 2 P

Page 104: 11X1 T05 01 permutations I (2011)

Sophia has five coloured blocks: one red, one blue, one green, one yellow and one white.

She stacks two, three, four or five blocks on top of one another to form a vertical tower.

2006 Extension 1 HSC Q3c)

(i) How many different towers are there that she could form that are three blocks high?

35 Towers P60

(ii) How many different towers can she form in total?

25 Towersblock 2 P 20

Page 105: 11X1 T05 01 permutations I (2011)

Sophia has five coloured blocks: one red, one blue, one green, one yellow and one white.

She stacks two, three, four or five blocks on top of one another to form a vertical tower.

2006 Extension 1 HSC Q3c)

(i) How many different towers are there that she could form that are three blocks high?

35 Towers P60

(ii) How many different towers can she form in total?

25 Towersblock 2 P

35 Towersblock 3 P

20

Page 106: 11X1 T05 01 permutations I (2011)

Sophia has five coloured blocks: one red, one blue, one green, one yellow and one white.

She stacks two, three, four or five blocks on top of one another to form a vertical tower.

2006 Extension 1 HSC Q3c)

(i) How many different towers are there that she could form that are three blocks high?

35 Towers P60

(ii) How many different towers can she form in total?

25 Towersblock 2 P

35 Towersblock 3 P

20

60

Page 107: 11X1 T05 01 permutations I (2011)

Sophia has five coloured blocks: one red, one blue, one green, one yellow and one white.

She stacks two, three, four or five blocks on top of one another to form a vertical tower.

2006 Extension 1 HSC Q3c)

(i) How many different towers are there that she could form that are three blocks high?

35 Towers P60

(ii) How many different towers can she form in total?

25 Towersblock 2 P

35 Towersblock 3 P

20

60

45 Towersblock 4 P

Page 108: 11X1 T05 01 permutations I (2011)

Sophia has five coloured blocks: one red, one blue, one green, one yellow and one white.

She stacks two, three, four or five blocks on top of one another to form a vertical tower.

2006 Extension 1 HSC Q3c)

(i) How many different towers are there that she could form that are three blocks high?

35 Towers P60

(ii) How many different towers can she form in total?

25 Towersblock 2 P

35 Towersblock 3 P

20

60

45 Towersblock 4 P 120

Page 109: 11X1 T05 01 permutations I (2011)

Sophia has five coloured blocks: one red, one blue, one green, one yellow and one white.

She stacks two, three, four or five blocks on top of one another to form a vertical tower.

2006 Extension 1 HSC Q3c)

(i) How many different towers are there that she could form that are three blocks high?

35 Towers P60

(ii) How many different towers can she form in total?

25 Towersblock 2 P

35 Towersblock 3 P

20

60

45 Towersblock 4 P 120

55 Towersblock 5 P

Page 110: 11X1 T05 01 permutations I (2011)

Sophia has five coloured blocks: one red, one blue, one green, one yellow and one white.

She stacks two, three, four or five blocks on top of one another to form a vertical tower.

2006 Extension 1 HSC Q3c)

(i) How many different towers are there that she could form that are three blocks high?

35 Towers P60

(ii) How many different towers can she form in total?

25 Towersblock 2 P

35 Towersblock 3 P

20

60

45 Towersblock 4 P 120

55 Towersblock 5 P 120

Page 111: 11X1 T05 01 permutations I (2011)

Sophia has five coloured blocks: one red, one blue, one green, one yellow and one white.

She stacks two, three, four or five blocks on top of one another to form a vertical tower.

2006 Extension 1 HSC Q3c)

(i) How many different towers are there that she could form that are three blocks high?

35 Towers P60

(ii) How many different towers can she form in total?

25 Towersblock 2 P

35 Towersblock 3 P

20

60

45 Towersblock 4 P 120

55 Towersblock 5 P 120

320Towersofnumber Total

Page 112: 11X1 T05 01 permutations I (2011)

Sophia has five coloured blocks: one red, one blue, one green, one yellow and one white.

She stacks two, three, four or five blocks on top of one another to form a vertical tower.

2006 Extension 1 HSC Q3c)

(i) How many different towers are there that she could form that are three blocks high?

35 Towers P60

(ii) How many different towers can she form in total?

25 Towersblock 2 P

35 Towersblock 3 P

20

60

45 Towersblock 4 P 120

55 Towersblock 5 P 120

320Towersofnumber Total

Exercise 10E; odd (not 39)