The number of ways of arranging all the lette | vedclass

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Question

(D) The word "$SUNITHA$" has $7$ letters: $S, U, N, I, T, H, A$. The vowels are $U, I, A$ ($3$ vowels). The consonants are $S, N, T, H$ ($4$ consonant

Vedclass · Accepted Answer

$144$

Vedclass · Answer

(D) The word "$SUNITHA$" has $7$ letters: $S, U, N, I, T, H, A$. The vowels are $U, I, A$ ($3$ vowels). The consonants are $S, N, T, H$ ($4$ consonants). There are $7$ positions. The vowels must occupy the $1^{st}$,$4^{th}$ (middle),and $7^{th}$ (last) positions. Number of ways to arrange $3$ vowels in these $3$ positions is $3! = 3 	imes 2 	imes 1 = 6$. Number of ways to arrange $4$ consonants in the remaining $4$ positions is $4! = 4 	imes 3 	imes 2 	imes 1 = 24$. Total number of arrangements = $3! 	imes 4! = 6 	imes 24 = 144$.

The number of ways of arranging all the letters of the word "$SUNITHA$" so that the vowels always occupy the first,middle,and last places is

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