The number of words which can be made out of | vedclass

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Question

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

Vedclass · Accepted Answer

$36$

Vedclass · Answer

(B) The word $MOBILE$ consists of $6$ letters: $M, O, B, I, L, E$.There are $3$ consonants $(M, B, L)$ and $3$ vowels $(O, I, E)$.The word has $6$ positions: $1, 2, 3, 4, 5, 6$.The odd positions are $1, 3, 5$ (total $3$ positions).The even positions are $2, 4, 6$ (total $3$ positions).According to the condition,the $3$ consonants must occupy the $3$ odd positions,which can be done in ${}^3P_3 = 3! = 6$ ways.The remaining $3$ vowels must occupy the $3$ even positions,which can be done in ${}^3P_3 = 3! = 6$ ways.Therefore,the total number of words $= 6 	imes 6 = 36$.

The number of words which can be made out of the letters of the word $MOBILE$ when consonants always occupy odd places is

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