The number of permutations by taking all lett | vedclass

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(D) The word $COMBINE$ has $7$ letters: $C, O, M, B, I, N, E$.The vowels are $O, I, E$ ($3$ vowels).The consonants are $C, M, B, N$ ($4$ consonants).T

Vedclass · Accepted Answer

$576$

Vedclass · Answer

(D) The word $COMBINE$ has $7$ letters: $C, O, M, B, I, N, E$.The vowels are $O, I, E$ ($3$ vowels).The consonants are $C, M, B, N$ ($4$ consonants).There are $7$ positions in total. The odd positions are $1, 3, 5, 7$ ($4$ odd places).We need to place $3$ vowels in $4$ odd places, which can be done in $^4P_3$ ways.$^4P_3 = 4 	imes 3 	imes 2 = 24$ ways.The remaining $4$ letters (consonants) can be arranged in the remaining $4$ positions in $4!$ ways.$4! = 4 	imes 3 	imes 2 	imes 1 = 24$ ways.Total number of permutations $= ^4P_3 	imes 4! = 24 	imes 24 = 576$.

The number of permutations by taking all letters and keeping the vowels of the word $COMBINE$ in the odd places is

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