In how many ways can the letters of the word | vedclass

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(D) The word '$NUTAN$' has $5$ letters: $N, U, T, A, N$.Consonants are $N, T, N$ ($3$ letters) and vowels are $U, A$ ($2$ letters).There are $5$ posit

Vedclass · Accepted Answer

$6$

Vedclass · Answer

(D) The word '$NUTAN$' has $5$ letters: $N, U, T, A, N$.Consonants are $N, T, N$ ($3$ letters) and vowels are $U, A$ ($2$ letters).There are $5$ positions in total: $1, 2, 3, 4, 5$.Odd positions are $1, 3, 5$ ($3$ places) and even positions are $2, 4$ ($2$ places).Consonants $(N, T, N)$ must occupy the $3$ odd places. The number of ways to arrange them is $\frac{3!}{2!} = 3$ (since $N$ repeats twice).Vowels $(U, A)$ must occupy the $2$ even places. The number of ways to arrange them is $2! = 2$.Total number of arrangements $= 3 	imes 2 = 6$.

In how many ways can the letters of the word '$NUTAN$' be arranged when consonants occupy odd places and vowels come on even places?

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