Discussion

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: C

DETAIL has six distinct letters: vowels E, A, I and consonants D, T, L.

The odd positions are 1, 3 and 5 - three places for three vowels.

\[ \text{vowels} = 3! = 6 \]

\[ \text{consonants in the even positions} = 3! = 6 \]

\[ 6 \times 6 = 36 \]

The two counts match exactly, which is what makes the restriction satisfiable at all.

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