Permutations and Combinations Quiz Set 016 | Maths Aptitude Quiz Questions and Mock Test on Permutations and Combinations Set 16 | 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 'VIOLET' 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

Out of given 6 consonants and 4 vowels, how many words can be formed that contain 3 consonants and 2 vowels or 3 vowels and 2 consonants?

21600.

21610.

21590.

21620.

Soln.
Ans: a

We can make the selection in ⁴C₃ × ⁶C₂ + ⁴C₂ × ⁶C₃ ways. But the five members can themselves be arranged in 5! ways. So the number of words is 120 × (⁴C₃ × ⁶C₂ + ⁴C₂ × ⁶C₃) = 21600.