How many words,each of 3 vowels and 2 consona | vedclass

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(C) The word '$INVOLUTE$' contains $8$ distinct letters.The vowels in the word are $\{I, O, U, E\}$,which are $4$ in total.The consonants in the word

Vedclass · Accepted Answer

$2880$

Vedclass · Answer

(C) The word '$INVOLUTE$' contains $8$ distinct letters.The vowels in the word are $\{I, O, U, E\}$,which are $4$ in total.The consonants in the word are $\{N, V, L, T\}$,which are $4$ in total.We need to select $3$ vowels out of $4$ and $2$ consonants out of $4$.The number of ways to select the letters is $C(4, 3) 	imes C(4, 2) = 4 	imes 6 = 24$.These $5$ selected letters can be arranged among themselves in $5!$ ways.$5! = 5 	imes 4 	imes 3 	imes 2 	imes 1 = 120$.Therefore,the total number of words that can be formed is $24 	imes 120 = 2880$.

How many words,each of $3$ vowels and $2$ consonants,can be formed from the letters of the word '$INVOLUTE$'?

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