How many words can be formed out of the lette | vedclass

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Question

(B) The word '$EDUCATION$' contains $9$ letters: $E, D, U, C, A, T, I, O, N$.There are $5$ vowels $(E, U, A, I, O)$ and $4$ consonants $(D, C, T, N)$.

Vedclass · Accepted Answer

$2880$

Vedclass · Answer

(B) The word '$EDUCATION$' contains $9$ letters: $E, D, U, C, A, T, I, O, N$.There are $5$ vowels $(E, U, A, I, O)$ and $4$ consonants $(D, C, T, N)$.The positions are $1, 2, 3, 4, 5, 6, 7, 8, 9$. The odd positions are $1, 3, 5, 7, 9$ (total $5$ positions).The $5$ vowels can be arranged in these $5$ odd positions in $5!$ ways.$5! = 5 	imes 4 	imes 3 	imes 2 	imes 1 = 120$.The $4$ consonants can be arranged in the remaining $4$ even positions $(2, 4, 6, 8)$ in $4!$ ways.$4! = 4 	imes 3 	imes 2 	imes 1 = 24$.Therefore,the total number of words $= 5! 	imes 4! = 120 	imes 24 = 2880$.

How many words can be formed out of the letters of the word '$EDUCATION$' such that vowels occupy the odd positions?

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