Permutations and Combinations Worksheet

**Page 8**

71.

What is the value of (-3)!?

a. | 1 | ||

b. | 6 | ||

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.

(- 3)! is not defined.

Correct answer : (4)

72.

Marissa has 8 coats, 6 pair of shoes, 5 jewelry sets, and 3 watches. State whether the way she can dress up is a permutation or a combination.

a. | Combination | ||

b. | Permutation |

Marissa selects one from 8 coats, one from 6 pair of shoes, one from 5 jewelry sets, and one from 3 watches to dress up.

As order of selection does not matters, selection is always a combination.

So, the way Marissa can dress up is a combination.

Correct answer : (1)

73.

A detective wants to break a 3-lettered code, which has no repetition of alphabets. State whether the arrangement of alphabets in the code is a permutation or a combination.

a. | Combination | ||

b. | Permutation |

As different orders of same letters form different words, ordering of alphabets is important in finding the code.

So, the arrangement of alphabets in the code is a permutation.

Correct answer : (2)

74.

In how many ways can you distribute a king, a queen and a jack card to three persons?

a. | 2 | ||

b. | 3 | ||

c. | 1 | ||

d. | 6 |

The list of all possible distributions:

1

King Queen Jack

Jack King Queen

King Jack Queen

Jack Queen King

Queen Jack King

Queen King Jack

Total number of possible distributions = 6

A king, queen and a jack card can be distributed to 3 persons in 6 different ways.

Correct answer : (4)

75.

What is the value of $\frac{\mathrm{5!}}{\mathrm{3!\times 2!}}$ ?

a. | 10 | ||

b. | 6 | ||

c. | 2 | ||

d. | 30 |

[Expand 5!.]

5! = 5×4×3 × 2!

[Simplify 5!.]

3! = 3 ×2 ×1

[Expand 3!.]

[Substitute the values of 5! and 3!.]

=

[Divide the numerator and the denominator by 2!.]

= 10

[Simplify the fraction.]

The value of

Correct answer : (1)

76.

What is the value of $\frac{\mathrm{n!}}{\mathrm{n}}$?

a. | $n$ | ||

b. | 1! | ||

c. | ($n$ - 1)! | ||

d. | $n$! |

[Expand n!.]

[Substitute the value of

[Simplify.]

(

[Expansion of (

The value of

Correct answer : (3)

77.

What is the value of _{2}C_{5}?

a. | 5 | ||

b. | 2 | ||

c. | Not defined | ||

d. | 7 |

The value of

In

The value of

Correct answer : (3)

78.

How many meaningful 4-letter words are there in the list of all possible arrangements of the letters in the word EARN, if each letter is used only once?

a. | 5 | ||

b. | 1 | ||

c. | 3 | ||

d. | 2 |

The possible arrangements of the letters in the word EARN are

The meaningful words in the above list are EARN and NEAR.

There are 2 meaningful words in the list of all possible arrangements of the letters in the word EARN.

Correct answer : (4)

79.

What is the value of _{9}P_{2} + _{9}C_{2}?

a. | 108 | ||

b. | 36 | ||

c. | 118 | ||

d. | 72 |

[Expand and multiply.]

[Substitute the values of 2! and

[Simplify the product.]

[Substitute the values of

Correct answer : (1)

80.

What is the value of (_{4}P_{2})^{2}?

a. | 4 | ||

b. | 144 | ||

c. | 12 | ||

d. | 156 |

[Expand and multiply.]

(

[Substitute the value of

The value of (

Correct answer : (2)