(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 $6$

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(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 $= 3! \times 3! = 6 \times 6 = 36$.

Class 11 Mathematics Permutation and Combination Definition of permutation, Number of permutations with or without repetition, Conditional permutations

Medium

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

A
$20$
B
$36$
C
$30$
D
$720$

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Permutation and Combination

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

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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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