In how many ways can the letters of the word | vedclass

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Question

(B) The word $MULTIPLE$ consists of $8$ letters: $M, U, L, T, I, P, L, E$. The vowels are $U, I, E$ and the consonants are $M, L, T, L$. The vowels ar

Vedclass · Accepted Answer

$360$

Vedclass · Answer

(B) The word $MULTIPLE$ consists of $8$ letters: $M, U, L, T, I, P, L, E$. The vowels are $U, I, E$ and the consonants are $M, L, T, L$. The vowels are at positions $2, 5, 8$. Keeping these positions fixed,the $3$ vowels can be arranged in $3! = 6$ ways. The remaining $5$ positions are occupied by the consonants $M, L, T, L$. The number of ways to arrange these $5$ consonants (where $L$ repeats twice) is $\frac{5!}{2!} = \frac{120}{2} = 60$. Therefore,the total number of arrangements is $3! 	imes 60 = 6 	imes 60 = 360$.

In how many ways can the letters of the word $MULTIPLE$ be arranged keeping the position of the vowels fixed?

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