RAHIMI @ SESMA

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RAHIMI @ SESMA

LEARNING OBJECTIVES Students will be taught to:

1. Understand and use the concept of permutation.

Detail

RAHIMI @ SESMA

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RAHIMI @ SESMA

LEARNING OUTCOMES

Students will be able to: Determine the total number of ways to perform successive events using

multiplication rule.

Example : From SESMA to HSNZ There are 2 routes joining SESMA and BUKIT BESAR and 3

routes joining BUKIT BESAR and HSNZ.Find the number of different ways of traveling from SESMA

to HSNZ via BUKIT BESAR.

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RAHIMI @ SESMA

BUKIT BESAR

JAMBATAN

MANIRSESMA HSNZ

GONG KAPAS/BATU BURUK

JPJ/POLIS

GONG KAPAS / SMAK

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RAHIMI @ SESMA

SESMA

(1) JAMBATAN SULTAN MAHMUD

BUKIT BESAR

(3) GONG KAPAS / BATU BUROK

HSNZ(4) JPJ / POLIS

(2) MANIR (4) GONG KAPAS / SMA KHAIRIAH

Kemungkinan : Laluan 1 : (1) , (3) Laluan 2 : (1) , (4) Laluan 3 : (1) , (5)Laluan 4 : (2) , (3) Laluan 5 : (2) , (4) Laluan 6 : (2) , (5) Oleh itu : Terdapat 6 cara yang berbeza dari SESMA ke HSNZ Multiplication Rule : From SESMA to BUKIT BESAR = 2 cara

From BUKIT BESAR to HSNZ = 3 cara Bilangan cara = 2 x 3 = 6

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RAHIMI @ SESMA

There are 3 routes joining village A and village B and 4 routes joining village B and village C. Find the number of different ways of traveling from village A to village C via village B.

3 4 12cara

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RAHIMI @ SESMA

There are 2 bus companies that provide transport from town E to town F and 3 bus companies that provide transport from town F to town G. Find the number of ways a person can travel from town E via to town G via town F by taking a bus. 2 3 6cara

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RAHIMI @ SESMA

A B C D 1 2 3

The diagram above shows cards of a game. If a player is going to select a letter card and a digit card, find the number of different ways can this be done.

4 3 12cara

RAHIMI @ SESMA

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RAHIMI @ SESMA

LEARNING OUTCOMESStudents will be able to:

Determine the number of permutations of n different objects.

or

nnn

nPn

n

1!

!)(!

! ( 1)( 2)........(3)(2)(1)n n n n

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RAHIMI @ SESMA

The diagram below shows eight cards with different letters on it. Find the number of arrangements if all the cards are used without restriction.

C O M P U T E R

8 7 6 5 4 3 2 1

Number of arrangements = 8x7x6x 5x4x3x2x1 = 40 320

Or use ; = 40 32088P

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RAHIMI @ SESMA

In how many different ways can 5 different books be arranged on a shelf ?

In how many different ways can 4 different presents can be given to 4 children ?

5! 120 cara

4! 24 cara

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RAHIMI @ SESMA

In how many ways can the letters of the word ‘GRADIENT’ be arranged ?

How many five-digit numbers can be formed using the digits 2,3,7, 8 and 9 without repetition ?

8! 40320 cara

5! 120 cara

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RAHIMI @ SESMA

LEARNING OUTCOMESStudents will be able to:

Determine the number of permutations of n different objects taken r at a time for given conditions.

!

( )!nr

nPn r

RAHIMI @ SESMA

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RAHIMI @ SESMA

RAHIMI @ SESMA

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RAHIMI @ SESMA

How many four-digit numbers can you form using the digits 2, 3, 5, 6 and 7 ?

45 120P cara

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RAHIMI @ SESMA

1 2 4 6

4 keping kad bernombor disusun

3 keping kad bernombor disusun

Berapa nombor ganjil 3 digit yang boleh dibentuk ?

4! 24 cara

34 24P cara

1 21 3 6P P cara

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1 2 4 6

Berapa nombor genap 4 digit yang boleh dibentuk ? Berapa nombor genap 3 digit yang boleh dibentuk ?

Berapa nombor ganjil 4 digit > 3000 yang boleh dibentuk ?

33 3 18P cara

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RAHIMI @ SESMA

LATIHAN : 5AB, 5UO

BOOSTER – PAGE 79 & 80

TEXT BOOK – PAGE 153 Q2, Q3, Q5, Q7, Q8, Q9

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RAHIMI @ SESMA

Diagram below shows eight letter cards. A five-letter code is to be formed using five of these cards. Find the number of different five-letter codes that can be formed which start with a vocal.

B O C D U F A V

7 6 5 4

Number of arrangement = 3x7x6x 5x4 = 2520 or use = = 25204

71

3 PP

3

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RAHIMI @ SESMA

Diagram below shows eight letter cards. A five-letter code is to be formed using five of these cards. Find the number of different five-letter codes that can be formed which start with letter “X” and end with letter “O”.

A P E X S O F T

6 5 4 1

Number of arrangement = 1x6x5x4x1 = 120 or use, = 1203

6P

1

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RAHIMI @ SESMA

Diagram below shows seven cards with different digits. Find the number of 4-digit numbers that can be form if the number formed is an even number.

1 2 3 4 5 6 7

6 5 4 3

Numbers can be form = 6x5x4x3 = 360 or use , = 3601

33

6 PP

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RAHIMI @ SESMA

A 4 - digit number is to be formed from digits 0, 1, 2, 3, 4, 5 and 6 without using any digit more than once. Find the number of possible four-digits numbers that can be formed if the number formed is greater than 2 500.

0 1 2 3 4 5 6

4

Number can be formed = 1x2x5x4 = 40 or use ; = 402

51

21

1 PPP

1 2 5

Case 1

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RAHIMI @ SESMA

A 4 - digit number is to be formed from digits 0, 1, 2, 3, 4, 5 and 6 without using any digit more than once. Find the number of possible four-digits numbers that can be formed if the number formed is greater than 2 500.

0 1 2 3 4 5 6

4

Number can be formed= 4x6x5x4 = 480 Or use ; = 4803

61

4 PP

4 6 5

Case 2

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RAHIMI @ SESMA

A 4 - digit number is to be formed from digits 0, 1, 2, 3, 4, 5 and 6 without using any digit more than once. Find the number of possible four-digits numbers that can be formed if the number formed is greater than 2 500.

Numbers can be formed greater than 2 500.

= (4x6x5x4) + (1x2x5x4 )= 480 + 40 = 520

)()( 25

12

11

36

14 PPPPP =520

or

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RAHIMI @ SESMA

L1L2L2L1

Diagram belows shows 2 boys and 5 girls in a rows. Find the number of these arrangements in which the two boys are side by side.

L1 L2 G3 G4 G5 G6 G7

Number of arrangement for 2 boys = 22

2PL1L2

Number of arrangement for 6 boys = =720 6

6P Sum of arrangement = 2x720 = 1440

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RAHIMI @ SESMA

How many ordered arrangements are there if we want to arrange 5 out of 12 basket players ?

[95040]In how many different ways can 3 of the letters in the word ‘ PROGRAM ‘ be arranged without repetition ?

[210]

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RAHIMI @ SESMA

how many different ways can 2 of the letters in the word ‘ ‘be arranged without repetition ?

20]How many four-digit numbers can you form using the digits 2, 3, 5, 6 and 7 ?

120]

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RAHIMI @ SESMA