In how many different ways can the letters of | vedclass

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Question

(C) The word '$DETAIL$' consists of $6$ letters: $3$ vowels $(A, E, I)$ and $3$ consonants $(D, T, L)$.There are $6$ positions in total: $1, 2, 3, 4,

Vedclass · Accepted Answer

$36$

Vedclass · Answer

(C) The word '$DETAIL$' consists of $6$ letters: $3$ vowels $(A, E, I)$ and $3$ consonants $(D, T, L)$.There are $6$ positions in total: $1, 2, 3, 4, 5, 6$.The odd positions are $1, 3,$ and $5$ (total $3$ positions).The even positions are $2, 4,$ and $6$ (total $3$ positions).We need to place $3$ vowels in $3$ odd positions,which can be done in $3! = 6$ ways.We need to place $3$ consonants in $3$ even positions,which can be done in $3! = 6$ ways.Therefore,the total number of arrangements is $6 	imes 6 = 36$.

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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