SOLUTION: 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?

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Question 928821:
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?
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Each arrangement is of the form

VCVCVC

where V stands for a vowel and C for a consonant.  We can choose
the three vowels {E,A,I} to go where the V's are in 3!=6 ways.

For each of those 6 ways to arrange the vowels where the V's are,
we can arrange the 3 consonants (D,T,L) to go where the C's are
also in 3!=6 ways.

So there are 6*6 or 36 ways.  

Edwin