# Permutations and Combinations Quiz Set 020

### Question 1

The letters of the word 'HOLIDAY' have to be arranged such that the vowels come together. How many different ways are possible?

A

720.

B

730.

C

710.

D

740.

Soln.
Ans: a

This word has 7 letters, out of which 4 are consonants and 3 are vowels. The vowels have to occupy three contiguous positions. This triad can be arranged in 3! ways like this: we can place 3 vowels in first place, 2 in second place and 1 in the third place, giving 3 × 2 × 1 = 6 permutations. Next, we have to arrange the 4 consonants and the triad treated as one letter, giving 5! = 120 possibilities. So the total possibilities are 6 × 120 = 720.

### Question 2

From a group of 9 boys and 6 girls, in how many ways can 2 boys and 2 girls be selected?

A

540.

B

550.

C

530.

D

560.

Soln.
Ans: a

The required count is 6C2 × 9C2 = 540.

### Question 3

2 men are standing in front of 3 cabins. In how many ways can they enter the cabins?

A

6.

B

11.

C

4.

D

7.

Soln.
Ans: a

The first has 3 options, the second has (3 - 1), and so on. This is expressed as 3P2, which evaluates to 6.

### Question 4

What is the value of 8P2?

A

56.

B

66.

C

46.

D

76.

Soln.
Ans: a

8P2 is \${8 !}/{(8 - 2) !}\$ = 56.

### Question 5

How many words can be formed with 7 distinct consonants and 4 distinct vowels such that vowels stay together at the end of each word?

A

120960.

B

120970.

C

120950.

D

120980.

Soln.
Ans: a

We have to basically create two parts - one containing 7 consonants and the other containing 4 vowels. The consonants can be arranged in 7 ! ways, and vowels in 4 ! ways. The total count will be 7 ! × 4 ! = 120960.