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 one.
A) 120
B) 60
C) 48
D) 32
E) None of these
3 vowels can be arranged in three odd places in 3! ways.   Similarly, 3 consonants can be arranged in three even places in 3! ways.   Hence, the total number of words in which vowels occupy odd positions = 3! × 3! = 6 × 6 = 36 ways.   Answer None of these
<result>E</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?