How many words,with or without meaning,each o | vedclass

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Question

(A) In the word $INVOLUTE$,there are $4$ vowels $(I, O, U, E)$ and $4$ consonants $(N, V, L, T)$.The number of ways to select $3$ vowels out of $4$ is

Vedclass · Accepted Answer

$2880$

Vedclass · Answer

(A) In the word $INVOLUTE$,there are $4$ vowels $(I, O, U, E)$ and $4$ consonants $(N, V, L, T)$.The number of ways to select $3$ vowels out of $4$ is $^{4}C_{3} = 4$.The number of ways to select $2$ consonants out of $4$ is $^{4}C_{2} = 6$.The total number of combinations of $3$ vowels and $2$ consonants is $4 	imes 6 = 24$.Each combination of $5$ letters can be arranged in $5!$ ways.Therefore,the total number of words is $24 	imes 5! = 24 	imes 120 = 2880$.

How many words,with or without meaning,each of $3$ vowels and $2$ consonants can be formed from the letters of the word $INVOLUTE$?

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