Permutations and Combinations Worksheet

**Page 4**

31.

What is the value of the expression $\frac{180}{{}_{5}{\mathrm{P}}_{3}}$?

a. | 4 | ||

b. | 3 | ||

c. | 5 | ||

d. | None of the above |

[Expand

[Substitute the value of

The value of

Correct answer : (2)

32.

What is the value of 5!?

a. | 5 | ||

b. | 124 | ||

c. | 120 | ||

d. | 11 | ||

e. | 13 |

5! = 5 × 4 × 3 × 2 × 1

[Expand 5!.]

5! = 120

[Multiply.]

The value of 5! is 120.

Correct answer : (3)

33.

Find the number of ways of choosing 4 members from a team of 15 members.

a. | 179 | ||

b. | 1365 | ||

c. | 1265 | ||

d. | 169 |

[Expand

[Expand

4! = 4 × 3 × 2 × 1 = 24

[Expand 4!.]

[Substitute the values of 4! and

= 15 × 7 × 13 = 1365

[Simplify.]

Number of ways of choosing 4 members from a team of 15 members = 1365

Correct answer : (2)

34.

What is the value of 2! + 5!?

a. | 127 | ||

b. | 124 | ||

c. | 122 | ||

d. | None of the above |

[Expand 2! and multiply.]

5! = 5 ×4 ×3 ×2 ×1 = 120

[Expand 5! and multiply.]

2! + 5! = 2 + 120 = 122

[Substitute and add.]

The value of (2! + 5!) is 122.

Correct answer : (3)

35.

In how many ways can 7 books be arranged in a shelf?

a. | 8! | ||

b. | _{7}C_{7} | ||

c. | 7 ^{7} | ||

d. | 7! |

Number of ways in which 7 books can be arranged =

There are 7! ways to arrange 7 books in a shelf.

Correct answer : (4)

36.

Evaluate: 4! × (1! + 0!)

a. | 53 | ||

b. | 50 | ||

c. | 48 | ||

d. | 49 |

[Expand 4! and multiply.]

1! + 0! = 1 + 1 = 2

[Substitute 1! = 1 and 0! = 1.]

4! x (1! + 0!) = 24 x 2 = 48

[Substitute the values of 4! and (1! + 0!).]

Correct answer : (3)

37.

What is the value of $\frac{9!}{(9-2)!}$?

a. | 75 | ||

b. | 72 | ||

c. | 66 | ||

d. | 77 | ||

e. | 144 |

[Expand 9!.]

(9 - 2)! = 7!

[Simplify.]

[Substitute the values of 9! and (9 - 2)!.]

= 9 × 8 = 72

[Simplify.]

The value of

Correct answer : (2)

38.

Marissa has 5 different toys and wants to display 3 of them. In how many ways can they be selected and arranged?

a. | 30 | ||

b. | 20 | ||

c. | 55 | ||

d. | 60 |

Number of ways in which 3 toys can be arranged = 3!

Number of ways in which 3 out of 5 toys can be selected and arranged =

=

[Simplify.]

There are 60 different ways to select 3 of the 5 toys and arrange them for display.

Correct answer : (4)

39.

Find the number of arrangements of the letters of the word MATH.

a. | 12 | ||

b. | 24 | ||

c. | 9 | ||

d. | 10 |

There are 4 letters to put in the first place, 3 letters to put in the second place, 2 letters to put in the third place and 1 letter to put in the fourth place.

By counting principle, number of arrangements = 4 × 3 × 2 × 1 = 24.

The letters of the word 'MATH' can be arranged in 24 different ways.

Correct answer : (2)

40.

A 13-member club is choosing its President, Vice president, Secretary and Treasurer. Find the number of ways in which they can be chosen.

a. | 156 | ||

b. | 1320 | ||

c. | 1716 | ||

d. | 17160 |

From the counting principle, the four people can be chosen in 13 x 12 x 11 x 10 ways.

= 17160

[Multiply.]

There are 17160 different ways in which they can be chosen.

Correct answer : (4)