# Permutations and Combinations Quiz Set 011

### Question 1

5 men are standing in front of 7 cabins. In how many ways can they enter the cabins?

A

2520.

B

2525.

C

2518.

D

2521.

Soln.
Ans: a

The first has 7 options, the second has (7 - 1), and so on. This is expressed as 7P5, which evaluates to 2520.

### Question 2

In how many ways can a secretary and general secretary be chosen from a committee of 17 members?

A

272.

B

277.

C

270.

D

273.

Soln.
Ans: a

The secretary can be any of the 17 members, the general-secretary can then be any of the (17 - 1) members. So the answer is 17 × (17 - 1) = 272.

### Question 3

How many 5 digit numbers ending in 0 can be formed with a given set of 5 distinct digits none of which is 0? Repetition of digits is not allowed.

A

120.

B

130.

C

150.

D

140.

Soln.
Ans: a

The units place is blocked by zero. The tens place has 5 options, the hundreds place also has (5 - 1) options, and so on. This is expressed as 5 × 4 × 3 × 2 × 1, which evaluates to 120.

### Question 4

The letters of the word 'JUPITER' 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 5

There are 5 trains between two stations A and B. In how many ways can a student go from A to B and return by any of the available trains?

A

25.

B

30.

C

23.

D

26.

Soln.
Ans: a

The upward journey is possible in 5 ways, and the downward also in 5 ways. So the outcomes are 5 × 5 = 25.