# Permutations and Combinations Quiz Set 007

### Question 1

The letters of the word 'JOURNEY' 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 4 men and 6 women, in how many ways can 3 men and 2 women or 2 men and 3 women be selected?

A

180.

B

190.

C

170.

D

200.

Soln.
Ans: a

The required count is 6C3 × 4C2 + 6C2 × 4C3 = 180.

### Question 3

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.

### Question 4

How many 4 digit numbers can be formed with a given set of 7 distinct digits?

A

2401.

B

2411.

C

2431.

D

2421.

Soln.
Ans: a

The first place has 7 options, the second place also has 7 options, and so on. This is expressed as 7 × 7 × 7 × 7, which evaluates to 2401.

### Question 5

In how many ways can 4 prizes be given to 3 students if each of them is equally eligible?

A

64.

B

74.

C

94.

D

84.

Soln.
Ans: a

The first has 4 options, the second also has 4 options, and so on. This is expressed as 4 × 4 × 4, which evaluates to 64. 