Aptitude Hack#36(31-3-19)

Question:

In how many different ways can the letters of the word 'DETAIL' be arranged in such a way that the vowels occupy only the odd positions?

A) 32

B) 48

C) 36

D) 60

Answer C)36

Explanation:

There are 6 letters in the given word, out of which there are 3 vowels and 3 consonants.
Let us mark these positions as under:       

1

2

3

4

5

6

Now, 3 vowels can be placed at any of the three places out 4, marked 1, 3, 5.
Number of ways of arranging the vowels = 3P3 = 3! = 6.
Also, the 3 consonants can be arranged at the remaining 3 positions.
Number of ways of these arrangements = 3P3 = 3! = 6.
Total number of ways
= (6 x 6) = 36.