The number of arrangements of the word KANGAR | vedclass

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Question

(D) The word $KANGAROO$ contains $8$ letters: $K, A, N, G, A, R, O, O$. The letter $A$ appears $2$ times and $O$ appears $2$ times.Total number of arr

Vedclass · Accepted Answer

$7560$

Vedclass · Answer

(D) The word $KANGAROO$ contains $8$ letters: $K, A, N, G, A, R, O, O$. The letter $A$ appears $2$ times and $O$ appears $2$ times.Total number of arrangements $= \frac{8!}{2!2!} = \frac{40320}{4} = 10080$.To find the number of arrangements where $A$'s do not appear together,we subtract the arrangements where $A$'s are together from the total.Treating the two $A$'s as a single unit $(AA)$,we have $7$ units: $(AA), K, N, G, R, O, O$.The number of arrangements where $A$'s are together $= \frac{7!}{2!} = \frac{5040}{2} = 2520$.Therefore,the number of required arrangements $= 10080 - 2520 = 7560$.

The number of arrangements of the word $KANGAROO$ in which $A$'s do not appear together is

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