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(D) The word $MATHEMATICS$ contains $11$ letters in total.The frequency of each letter is as follows:$M$ appears $2$ times.$A$ appears $2$ times.$T$ a

Vedclass · Accepted Answer

$\frac{11!}{8}$

Vedclass · Answer

(D) The word $MATHEMATICS$ contains $11$ letters in total.The frequency of each letter is as follows:$M$ appears $2$ times.$A$ appears $2$ times.$T$ appears $2$ times.$H, E, I, C, S$ appear $1$ time each.The number of ways to arrange $n$ objects where $n_1, n_2, ...$ are the frequencies of repeating objects is given by the formula $\frac{n!}{n_1! 	imes n_2! 	imes ...}$.Substituting the values: $\frac{11!}{2! 	imes 2! 	imes 2!} = \frac{11!}{2 	imes 2 	imes 2} = \frac{11!}{8}$.

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

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