In how many different ways can the letters of | vedclass

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Question

(C) The word '$KURUKSHETRA$' contains $11$ letters in total.The frequency of each letter is as follows:$K$ appears $2$ times.$U$ appears $2$ times.$R$

Vedclass · Accepted Answer

$4989600$

Vedclass · Answer

(C) The word '$KURUKSHETRA$' contains $11$ letters in total.The frequency of each letter is as follows:$K$ appears $2$ times.$U$ appears $2$ times.$R$ appears $2$ times.$S, H, E, T, A$ appear $1$ time each.The number of ways to arrange $n$ objects where $n_1, n_2, n_3$ are the frequencies of identical objects is given by $\frac{n!}{n_1! n_2! n_3!}$.Therefore,the required number of arrangements $= \frac{11!}{2! 2! 2!} = \frac{39916800}{2 	imes 2 	imes 2} = \frac{39916800}{8} = 4989600$.

In how many different ways can the letters of the word '$KURUKSHETRA$' be arranged?

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