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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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There are 3 vowels(E, A, I) and 3 consonants(D, T, L).
The vowels can be placed in 1st, 3rd anf 5th position in 3P3 ways. Similarly the three consonants can be placed in the rest 3 places in 3P3 ways.

Total ways = 3P3 * 3P3 = 3! * 3! = 6*6 = 36
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