# Form 5 : Chapter 6 Permutations and Combinations 6 permutations and combinations

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• CHAPTER 6 PERMUTATIONS AND COMBINATIONS FORM 5

116

PAPER 1

1. A committee of 3 boys and 3 girls are to be formed from 10 boys and 11 girls.

In how many ways can the committee be formed?

[2 marks]

2. 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?

[2 marks]

3. Find the number of ways of choosing 6 letters including the letter G from the word

'GRACIOUS'.

[2 marks]

4. How many 3-digit numbers that are greater than 400 can be formed using the digits 1, 2, 3, 4,

and 5 without repetition?

[2 marks]

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

repetition?

[2 marks]

6. 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 ?

[3 marks]

7. A badminton team consists of 8 students. The team will be chosen from a group of 8 boys and 5 girls. Find the number of teams that can be formed such that each team consists of

a) 5 boys, b) not more than 2 girls.

[4 marks]

8. 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.

[4 marks]

A B C D 5 6 7 8

R A J I N

• CHAPTER 6 PERMUTATIONS AND COMBINATIONS FORM 5

117

9. A debating team consists of 6 students. These 6 students are chosen from 2 monitors, 3 assistant monitors and 5 prefects.

a) there is no restriction,

b) the team contains only 1 monitor and exactly 3 prefects.

[4 marks]

10. 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.

[4 marks]

11. 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?

[4 marks]

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

digit being repeated?

[4 marks]

13. A coach wants to choose 9 players consisting of 6 boys and 3 girls to form a squash team.

These 9 players are chosen from a group of 8 boys and 6 girls. Find

(a) the number of ways the team can be formed,

(b) the number of ways the team members can be arranged in a row for a group photograph,

if the 6 boys sit next to each other. [4 marks]

14. 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.

[3 marks]

15. Diagram shows six numbered cards.

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]

R O F I N U M

9 8 7 5 4 1

• CHAPTER 6 PERMUTATIONS AND COMBINATIONS FORM 5

118

1. 3

10C x 311C 1

= 19800

1

2. 1

4 p x 37 p 1

= 840

1

3. 1 x 57C 1

= 21

1

4. 1

2 p x 24 p 1

= 24

1

5. 3

4 p x 12 p 1

= 48

1

6. 34 p x 2

4 p 2

= 288

1

7. a) 58C x 3

5C = 560 1

b) If the team consists of 8 boys and 0 girl 88C x 0

5C = 1

If the team consists of 7 boys and 1 girl 78C x 1

5C = 40

If the team consists of 6 boys and 2 girl 68C x 2

5C = 280

1

The number of teams that can be formed = 1 + 40 + 280 1

= 321

1

8. a) 5! = 120 1

b) 4! x 2! 2

= 48

1

9. a) 610C = 210 2

b) 12C x 3

5C x 23C = 60 2

10. a) 57 p = 2520 2

b) 46 p x 1

4 p 1

= 1440

1

11. 1

5 p x 48 p 2

= 8400

1

12. 3

5 p x 13 p = 180 2

= 180

1

• CHAPTER 6 PERMUTATIONS AND COMBINATIONS FORM 5

119

13. a) 68C 3

6C 1

= 560 1

b) 6! x 4! 1

= 17280 1

14. 38 P x 2

2 P 2

= 672 1

15. a) 6P4 = 360

1

b) 5P3 x

4P1 2

= 240 1