(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

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(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 $4 \times 6 = 24$.Each combination of $5$ letters can be arranged in $5!$ ways.Therefore,the total number of words is $24 \times 5! = 24 \times 120 = 2880$.

Class 11 Mathematics Permutations and Combinations Definition of permutation, Number of permutations with or without repetition, Conditional permutations

Medium

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

A
$2880$
B
$1440$
C
$720$
D
$5760$

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Definition of permutation, Number of permutations with or without repetition, Conditional permutations

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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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