Permutations and Combinations Quiz Set 007 | Maths Aptitude Quiz Questions and Mock Test on Permutations and Combinations Set 7 | 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 'JOURNEY' have to be arranged such that the vowels come together. How many different ways are possible?

720.

730.

710.

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.

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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?

180.

190.

170.

200.

Soln.
Ans: a

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

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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?

120960.

120970.

120950.

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.

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