How many words can be formed with the letters | vedclass

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(C) 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

$\frac{11!}{2!2!2!}$

Vedclass · Answer

(C) 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 formula for the number of permutations of $n$ objects where $n_1, n_2, \dots, n_k$ are the frequencies of identical objects is given by $\frac{n!}{n_1! n_2! \dots n_k!}$.Substituting the values: $n = 11$,$n_1 = 2$ (for $M$),$n_2 = 2$ (for $A$),and $n_3 = 2$ (for $T$).Required number of words = $\frac{11!}{2! 2! 2!}$.

How many words can be formed with the letters of the word $MATHEMATICS$ by rearranging them?

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