Permutations and Combinations Quiz Set 001 | Maths Aptitude Quiz Questions and Mock Test on Permutations and Combinations Set 1 | mock tests for Bank PO, SSC Exams, SO Clerical Exam, GATE Exam, LIC AO, GIC AO, etc.

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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?

36.

46.

26.

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.

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Question 2

What is the value of ⁵C₃?

10.

20.

30.

Soln.
Ans: a

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

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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?

56.

61.

54.

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.

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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?

1440.

1450.

1430.

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.

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