Combinations Worksheet

**Page 1**

1.

a. | 9! | ||

b. | 9 | ||

c. | 1 |

[

=

= 1

[0! = 1.]

Correct answer : (3)

2.

A box contains 5 color pencils. How many different sets of 3 pencils can be chosen from it?

a. | 10 | ||

b. | 4 | ||

c. | 6 | ||

d. | 20 |

=

[

= 10

10 sets of 3 pencils can be formed.

Correct answer : (1)

3.

Find the number of ways of selecting 2 vowels and 2 consonants from the letters of the set {I, N, T, E, R, V, A, L}.

a. | 21 | ||

b. | 60 | ||

c. | 13 | ||

d. | 30 |

[The vowels in the set are I, E, A.]

The number of consonants = 5

[The consonants in the set are N, T, R, V, L.]

2 vowels can be selected from the 3 vowels in

2 consonants can be selected from the 5 consonents in

The number of ways of selecting 2 vowels and 2 consonants from the letters of the given set =

[Use the fundamental counting principle.]

=

[Use

=

[Simplify.]

The number of ways of selecting 2 vowels and 2 consonants from the letters of the given set = 30

Correct answer : (4)

4.

How many 4 card hands that contain exactly 3 aces and 1 queen can be chosen from a 52 card deck?

a. | 12 | ||

b. | 4 | ||

c. | 16 | ||

d. | 8 |

So, the number of 4 card hands that contain exactly 3 aces and 1 queen is (

=

[

=

[1! = 1.]

Correct answer : (3)

5.

If ${}_{n}\mathrm{C}{}_{2}$ = 28, then what is the value of $n$?

a. | 8 | ||

b. | 7, - 8 | ||

c. | - 7 | ||

d. | 8, - 7 |

[

(

[Factor.]

Correct answer : (1)

6.

Find the number of permutations of the elements in the set {F, O, U, R}.

a. | 3 | ||

b. | 4 | ||

c. | 6 | ||

d. | 24 |

The number of permutations of 4 distinct elements of the set is

= 4! = 24

[

Correct answer : (4)

7.

Find the number of permutations of the elements in the set {17, 19, 21, 23, 25, 27}.

a. | 25 | ||

b. | 720 | ||

c. | 162 | ||

d. | 150 |

Number of permutations of 6 distinct elements of the set is

= 6! = 6 · 5 · 4 · 3 · 2 · 1 = 720

[

Correct answer : (2)

8.

Find the number of 8 letter permutations from the letters of the word KEYBOARD .

a. | 40320 | ||

b. | 1 | ||

c. | 8 | ||

d. | 64 |

[Write the number of letters of the word.]

The number of 8 letter permutations from the 8 distinct letters of the word is

[

The number of 8 letter permutations from the 8 distinct letters of the word KEYBOARD is 40320.

Correct answer : (1)

9.

In how many ways can 2 different books be arranged on a shelf?

a. | 2! | ||

b. | 3! | ||

c. | 5! | ||

d. | 4! |

= 2!

[

Correct answer : (1)

10.

How many different 2 digit numbers can be formed using {2, 3, 4, 5, 6, 7, 8}, if repetition of a digit is not allowed?

a. | 120 | ||

b. | 42 | ||

c. | 72 | ||

d. | 5040 |

[

=

Correct answer : (2)