D. 36
Feedback The word 'DETAIL' has 6 letters which has 3 vowels (EAI) and 3 consonants(DTL)
The 3 vowels(EAI) must occupy only the odd positions. Let's mark the positions as (1) (2) (3) (4) (5) (6). Now, the 3 vowels should only occupy the 3 positions marked as (1),(3) and (5) in any order.
Hence, number of ways to arrange these vowels
= 3P3
= 3!=3×2×1=6
Now we have 3 consonants(DTL) which can be arranged in the remaining 3 positions in any order. Hence, number of ways to arrange these consonants
= 3P3
=3!=3×2×1=6
Total number of ways
= number of ways to arrange the vowels × number of ways to arrange the consonants
=6×6=36