# Permutations and Combinations Quiz Set 009

### Question 1

3 men are standing in front of 4 cabins. In how many ways can they enter the cabins?

A

24.

B

29.

C

22.

D

25.

Soln.
Ans: a

The first has 4 options, the second has (4 - 1), and so on. This is expressed as 4P3, which evaluates to 24.

### Question 2

There are 3 trains between two stations A and B. In how many ways can a student go from A to B and return by a different train?

A

6.

B

11.

C

4.

D

7.

Soln.
Ans: a

The upward journey is possible in 3 ways, and the downward in 2 ways. So the outcomes are 3 × 2 = 6.

### Question 3

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 a different train?

A

20.

B

25.

C

18.

D

21.

Soln.
Ans: a

The upward journey is possible in 5 ways, and the downward in 4 ways. So the outcomes are 5 × 4 = 20.

### Question 4

The letters of the word 'PICTURE' 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

Section A of an exam has 3 questions, B has 6 questions and C has 4 questions. In how many ways can a student attempt the paper if he has to select one question from each of these sections?

A

72.

B

77.

C

70.

D

73.

Soln.
Ans: a

Clearly, it is 3 × 6 × 4 = 72.

This Blog Post/Article "Permutations and Combinations Quiz Set 009" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2017-04-07.

Posted by Parveen(Hoven),
Aptitude Trainer