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
• E. 120

Answer 1

The correct option is C 36

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 = ${}^3{P}_3=3!=6$.
Also, the 3 consonants can be arranged at the remaining 3 positions.
Number of ways of these arrangements = ${}^3{P}_3=3!=6$.
Total number of ways = (6 x 6) = 36.