Permutations and Combinations Worksheet

**Page 9**

81.

Which of the following is true for any positive number?

a. | ($n$-1)! = $n$!- 1! | ||

b. | $n$! = $n$ | ||

c. | $n$! = $n$ x ($n$-1) x ($n$-2) x ($n$ - 3) x . . . x 1 | ||

d. | None of the above |

The value of

Correct answer : (3)

82.

Find the value of $r$, if _{3}P_{2} + $r$ x _{3}C_{2} = 0.

a. | -2 | ||

b. | -3 | ||

c. | 2 | ||

d. | 1 |

[Original equation.]

[Expand

6 +

[Substitute

6 +

[Cancel 6 with 2.]

[Subtract -6 from each side.]

[Divide each side by 3.]

The value of

Correct answer : (1)

83.

What is the value of the expression 60/(_{5}P_{3})?

a. | 2 | ||

b. | 3 | ||

c. | 1 | ||

d. | None of the above |

[Expand

60/(

[Substitute the value of

The value of 60/(

Correct answer : (3)

84.

Evaluate: 2! x (1! + 0!)

a. | 9 | ||

b. | 4 | ||

c. | 6 | ||

d. | 5 |

[Expand 2! and multiply.]

1! + 0! = 1 + 1 = 2

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

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

[Substitute the values of 2! and (1! + 0!).]

Correct answer : (2)

85.

In how many ways can 7 people sit in 7 chairs?

a. | 5041 | ||

b. | 720 | ||

c. | 5040 | ||

d. | 40320 |

= 7! = 7 ×6 ×5 ×4 ×3 ×2 ×1 = 5040

[Simplify.]

7 people can sit in 7 chairs in 5040 ways.

Correct answer : (3)

86.

In how many ways can 9 questions be selected out of 14 questions such that the selection always contains the questions numbered 1, 4 and 9?

a. | 472 | ||

b. | 452 | ||

c. | 467 | ||

d. | 462 |

Number of questions remaining after selecting questions numbered 1, 4 and 9 = 14 - 3 = 11

The remaining 6 questions have to be selected from these remaining 11 questions.

Number of ways in which 6 questions can be selected out of 11 questions =

6! = 6 ×5 ×4 ×3 ×2 ×1 = 720

[Expand 6! and multiply.]

[Expand

[Substitute the values of 6! and

The number of ways in which 9 questions can be selected out of 14 questions, always selecting questions numbered 1, 4 and 9 is 462.

Correct answer : (4)

87.

A teacher wants 4 of her 10 students to write a skill test. In how many ways can she select 4 students?

a. | 210 | ||

b. | 220 | ||

c. | 215 | ||

d. | 205 |

[Expand

[Expand

4! = 4 ×3 ×2 ×1 = 24

[Expand 4!]

[Substitute the values of 4! and

[Simplify the above product.]

The teacher can select 4 students out of 10 students in 210 ways.

Correct answer : (1)

88.

What is the value of _{4}P_{6}?

a. | 4 | ||

b. | 6 | ||

c. | Not defined | ||

d. | 24 |

The value of

In

The value of

Correct answer : (3)

89.

What is the value of (-2)!?

a. | 1 | ||

b. | 2 | ||

c. | Not defined |

The range of whole numbers is {0, 1, 2, 3, 4....}.

Negative numbers do not come in the range of whole numbers.

The factorial of a negative number is not defined.

(- 2)! is not defined.

Correct answer : (4)

90.

What is the value of (_{5}P_{2})^{2}?

a. | 410 | ||

b. | 800 | ||

c. | 420 | ||

d. | 400 |

[Expand and multiply.]

(

[Substitute the value of

The value of (

Correct answer : (4)