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?	Choose the correct option
A) 12  B) 14  C) 36  D) 38  E) 40
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.   ANSWER 36
<result>C</result>
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?