permutation 2010

Add. Math. Form 5: Chapter 6 Permutations and Combinations6.1 Permutations

6.1.1 Multiplication Rule

1. In how many ways can a man dress himself up from 4 different shirts and 3 different pairs of pants for a party.Number of ways of choosing a shirt =Number of ways choosing a pair of pants=Total number of ways of dressing up =

2. Ann plans to travel from Banting to Kuala Lumpur via Klang. From Banting to Klang, she has the options to travel by bus or taxi. From Klang to Kuala Lumpur, she has the options to travel by bus, taxi or train. Determine the different combination of modes of transport Ann can use to travel from Banting to Kuala Lumpur.

3. A restaurant offers the choice of a meat, a vegetable, a dessert and a drink for a lunch special. If there are 4 types of meat, 3 vegetables, 5 desserts and 2 drinks available to choose from, how many different lunch sets are available?

4. A quiz consists of 10 true/false questions. How many different answer sheets are possible?

5. Rahim has 3 options of selecting a city to be visited from tour package A and 5 options from tour package B. If he going to select a city from each package, in how many different ways can this be done?

6. There are 2 routes joining towns A and B and 5 routes joining towns B and C. Find the number of different ways of travelling from town A to town C via town B.

6.1.2 Permutations of n different objects

1. How many different ways can the alphabets in the word ‘SUN’ be arranged?

2. How many different ways can 6 different paintings be arranged in a row on a wall?

3. In how many different ways can 12 different books be arranged in a row on a shelf?

4. In how many different ways can all the letters in the word ‘SMART’ be arranged without repetition?

5. In how many different ways can 7 students be seated in a row for the photo session?

6. How many 4-dgit numbers can be formed using the digits 1, 2, 3 and 4 without repetition?

7. In how many ways can all the letters in the word 8. Using the digits 1, 2, 3, 4, 5, 6, 7, 8 and 9, find the number

If event A happens in r ways and event B happens in s ways, then the number of ways that event A happens followed by event B, is r x s.

Permutation is the number of ways of arranging the object where the order of arrangement is important.

The number of permutation of n different objects is given by

=

“FRIENDLY’ be arranged without repetition? of 9-digit numbers that can be formed without repetition.

9. There are 10 rings of different colours. In how many ways can all the rings be arrange in a row?

10. Find the number of ways to arrange all the alphabets in the word “UNIVERSAL”

1. Find the number of different arrangements of the letters of the word BANANA.

2. Find the number of different arrangements of the letters of the word EVERMORE

3. Find the number of different arrangements of the letters of the word ZOOLOGI

4. Find the number of different arrangements of the letters of the word MENTERI

5. In a row of 7 books, 3 are the same. Find the number of different arrangements of boos that can be made.

6. How many 5-dgit numbers can be formed using the digits 1, 1, 3 ,4 and 5 without repetition?

7. How many 6-dgit numbers can be formed using the digits 1, 3, 3,5, 5 and 5 without repetition?

8. How many 7-dgit numbers can be formed using the digits 1, 2, ,4, 4, 4 ,5 and 5 without repetition?

6.1.3 Permutations of n different objects taken r at a time

1. How many 3-digit codes can be formed by using the digits 1,2,3, …,8 without repetition?

2. How many different 5-letter arrangements can be made from the letters of the word “COMPUTER” without repeating any of the letters?

3. There are 10 scouts in a group. In how many different ways can 4 scouts in the group be arranged in a line?

4. In how many different ways can 2 of the letters in the word “WISDOM” be arranged without repetition?

5. How many 4-digit numbers can be formed using the digits 1, 3, 5, 7 and 9 without repetition?

6. Find the number of 3-digit numbers that can be formed from the digit 1,2,3, 4,5 and 6 if repetition of digits are not

The number of permutations of n objects of which p of one type are alike, q of a second type are alike

=

The number of permutations of n objects taken r at a time is

allowed.

7. 20 students are vying for the 3 prizes offered in a Science quiz. How many possible ways are there of awarding the prizes to the top 3 winners?

8. There are 10 different books in a shelf. How many ways can 4 of them be arranged in a row?

9. State the number of ways to arrange 3 letters from the word “SMART” without repetition.

10. How many 4-digit numbers can be formed using the digits 1 to 9 without repetition?

6.1.4 Permutations of n different objects for given conditions. 6.1.5 Permutations of n different objects taken r at a time for given conditions 1. How many 3-digit number greater than 200 can be formed

from the digits 1, 2 and 3 without repetition?

Number of arrangement =

2. How many 5-digit even number can be formed from the digits 1, 2 , 3 ,4 and 5 without repetition?


3. How many 5-digit number greater than 30000 can be formed from the digits 1, 2, 3, 4 and 5 without repetition?


4. How many 4-digit odd number can be formed from the digits 2,3,5 and 7 without repetition?


5. Find the number of ways the letters from the word “SMILE” can be formed if the arrangements begin with a vowel?


6. Given 4 letters are chosen from the word “FAVOUR”, find the number of arrangements that end with the vowel.


7. How many 4-digit number less than 7000 can be formed from all the prime numbers between 1 and 10 without repetition?


8. How many4-digit number greater than 4000 can be formed from all the prime numbers between 1 and 10 without repetition?


9. How many 3-digit odd number can be formed from the digits 1to 9 without repetition?


10. How many 3-digit even number can be formed from the digits 1, 2 , 3, 4 and 5 without repetition?


11. 5 boys and 3 girls are to be seated in a row. Calculate the number of possible arrangements if the 5 boys have to be

12. How many 5-digit number can be formed from the digits 1, 2 ,3, 4 and 5 without repetition, if the digit 1 and 4 must be

seated together.


arrange together??


13. 3 boys and 2 girls are to be seated in a row. Calculate the number of possible arrangements (a) if two boys have to be seated at the ends.

(b) If the two girls have to be seated together.

14. All the letters from the word “MOTHER” are to be arranged. Calculate the number of possible arrangements if the arrangement begins with the letter “K”

(a) the letters O and E must be arranged side by side.

15. The diagram shows 5 letters and 3 digits.

A code is to be formed using those letters and digits. The code must consists of 3 letters followed by 2 digits. How many codes can be formed if no letter or digit is repeateed in each code?

(SPM2003/1/22)

16. The diagram shows five cards of different letters.

(a) Find the number of possible arrangements, in arow, of all the crds.

(b) Find the number of these arrangement in which the letters E and A are side by side..

(SPM2004/1/23)

17. Diagram shows seven letter cards.

U N I F O R M

A four-letter code is to be formed using four of these cards.Find (a) the number of different four-letter codes that can be

formed,(b) the number of different four-letter codes which end

with a consonant. [4 marks](SPM2006/P1/22)

18. Diagram shows six numbers cards.

3 5 6 7 8 9

A four –digit number is to be formed by using four of these cards.How many

(a) different numbers can be formed?(b) different odd numbers can be formed? [4 marks]

(SPM2008/P1/23)

19. Find the number of different arrangements of the letters of

the word MEXICO. Find the numbers of these arrangements(a) which begin with M,(b) which have the letter X at one end and the letter C at

the other end.(“O” level J03/2/7)

20. Find how many different odd 4-digit numbers less than 4000 can be made from the digits 1,2,3,4,5,6,7 if no digit may be repeated.

(“O” level N02/2/5)

A B C D E 6 7 8H E B A T

21. Calculate the number of different 6-digit numbers which can be formed using the digits 0,1,2,3,4,5 without repetition and assuming that a number cannot begin with 0.

(“O” level J02/1/6)

22. Calculate how many different 5-digit numbers can be formed from the 9 digits 1,2,3,4,5,6,7,8,9 used without repetition. .In how many of these 5-digit numbers will the digits 8 and 9 be adjacent.

(“O” level N96/2/17)

23. How many 4-letter codes can be formed using the letters in the word 'GRACIOUS' without repetition such that the first letter is a vowel?

24. How many 3-digit numbers that are greater than 400 can be formed using the digits 1, 2, 3, 4, and 5 without repetition?

25. How many 4-digit even numbers can be formed using the digits 1, 2, 3, 4, and 5 without repetition?

26. Diagram shows 4 letters and 4 digits.

A code is to be formed using those letters and digits. The code must consists of 3 letters followed by 2 digits. How many codes can be formed if no letter or digit is repeated in each code ?

27. Diagram shows five cards of different letters.

(a) Find the number of possible arrangements, in a row, of all the cards.

(b) Find the number of these arrangements in which the letters A and N are side by side.

28. Diagram shows seven letter cards.

A five-letter code is to be formed using five of these cards. Find(a) the number of different five-letter codes that can be

formed,(b) the number of different five-letter codes which end with a

consonant.

A B C D 5 6 7 8

R A J I NROFINU MM

29. How many 5-digit numbers that are greater than 50000 can be formed using the digits 1, 2, 3, 4, 5, 6, 7, 8, and 9 without repetition?

30. How many 4-digit even numbers can be formed using the digits 1, 2, 3, 4, 5 and 6 without any digit being repeated?

31. 2 girls and 8 boys are to be seated in a row of 5 chairs. Find the number of ways they can be seated if no two persons of the same sex are next to each other.

32. Diagram shows six numbered cards.

A four-digit number is to be formed by using four of these cards.

How manya) different numbers can be formed?b) different odd numbers can be formed?

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permutation 2010

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