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Question

(A) The word '$ORIENTAL$' contains $8$ letters in total.The vowels in the word are: $O, I, E, A$ (Total $4$ vowels).The consonants in the word are: $R

Vedclass · Accepted Answer

$576$

Vedclass · Answer

(A) The word '$ORIENTAL$' contains $8$ letters in total.The vowels in the word are: $O, I, E, A$ (Total $4$ vowels).The consonants in the word are: $R, N, T, L$ (Total $4$ consonants).There are $8$ positions in total: $1, 2, 3, 4, 5, 6, 7, 8$.The odd positions are $1, 3, 5, 7$ (Total $4$ positions).The vowels must occupy these $4$ odd positions. The number of ways to arrange $4$ vowels in $4$ positions is $P(4, 4) = 4! = 24$.The remaining $4$ positions $(2, 4, 6, 8)$ must be occupied by the $4$ consonants. The number of ways to arrange $4$ consonants in $4$ positions is $P(4, 4) = 4! = 24$.Therefore,the total number of words that can be formed is $4! 	imes 4! = 24 	imes 24 = 576$.

Find how many words can be formed out of the letters of the word '$ORIENTAL$' so that vowels always occupy the odd places.

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