In how many different ways can the letters of | vedclass

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

Vedclass · Accepted Answer

$36$

Vedclass · Answer

(C) The word '$DETAIL$' consists of $6$ letters: $D, E, T, A, I, L$.There are $3$ vowels $(E, A, I)$ and $3$ consonants $(D, T, L)$.The positions are $1, 2, 3, 4, 5, 6$.The odd positions are $1, 3,$ and $5$.The $3$ vowels must occupy these $3$ odd positions. The number of ways to arrange the vowels is $^3P_3 = 3! = 6$.The remaining $3$ consonants must occupy the $3$ even positions ($2, 4,$ and $6$). The number of ways to arrange the consonants is $^3P_3 = 3! = 6$.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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