How many words can be formed using the letter | vedclass

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Question

(B) The word $MOBILE$ has $6$ letters: $M, O, B, I, L, E$.Consonants are $M, B, L$ ($3$ letters) and vowels are $O, I, E$ ($3$ letters).There are $6$

Vedclass · Accepted Answer

$36$

Vedclass · Answer

(B) The word $MOBILE$ has $6$ letters: $M, O, B, I, L, E$.Consonants are $M, B, L$ ($3$ letters) and vowels are $O, I, E$ ($3$ letters).There are $6$ positions: $1, 2, 3, 4, 5, 6$.Odd positions are $1, 3, 5$ ($3$ positions) and even positions are $2, 4, 6$ ($3$ positions).Consonants must occupy odd positions,which can be done in $3!$ ways.Vowels must occupy the remaining even positions,which can be done in $3!$ ways.Total number of words $= 3! 	imes 3! = 6 	imes 6 = 36$.

How many words can be formed using the letters of the word $MOBILE$ such that the consonants always occupy odd positions?

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