Permutations and Combinations Quiz Set 001

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Question 1

The letters of the word 'BEAUTY' have to be arranged such that the vowels occupy only the odd positions. How many different ways are possible?

 A

36.

 B

46.

 C

26.

 D

56.

Soln.
Ans: a

This word has 6 letters, out of which 3 are consonants and 3 are vowels. The vowels have to occupy three fixed odd positions. We can place 3 vowels in first odd place, 2 in second odd place and 1 in the third odd place, giving 3 × 2 × 1 = 6 permutations. This will be done with the consonants also. So the total possibilities are 6 × 6 = 36.


Question 2

What is the value of 5C3?

 A

10.

 B

20.

 C

0.

 D

30.

Soln.
Ans: a

5C3 is ${5 !}/{(5 - 3) ! × 3 !}$ = 10.


Question 3

There are 8 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

56.

 B

61.

 C

54.

 D

57.

Soln.
Ans: a

The upward journey is possible in 8 ways, and the downward in 7 ways. So the outcomes are 8 × 7 = 56.


Question 4

How many words can be formed with 6 distinct consonants and 2 distinct vowels such that vowels stay together at the end of each word?

 A

1440.

 B

1450.

 C

1430.

 D

1460.

Soln.
Ans: a

We have to basically create two parts - one containing 6 consonants and the other containing 2 vowels. The consonants can be arranged in 6 ! ways, and vowels in 2 ! ways. The total count will be 6 ! × 2 ! = 1440.


Question 5

There are 6 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

30.

 B

35.

 C

28.

 D

31.

Soln.
Ans: a

The upward journey is possible in 6 ways, and the downward in 5 ways. So the outcomes are 6 × 5 = 30.


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This Blog Post/Article "Permutations and Combinations Quiz Set 001" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2017-08-12.

Posted by Parveen(Hoven),
Aptitude Trainer


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