In how many ways can be letters of word ASSASSINATION be arranged so that all the S's are together?

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Solution

Considering all the S' together we get

$A A A N N I I T O (S S S S)$

The above alphabets in which repetition of A is 3 times, N is 2 times and I is 2 times,can be arranged in

$\frac{10!}{3! 2! 2!}$ .... where all the S' remain as a pack.

$= 151200$ ways.

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In how many ways can be letters of the word ASSASSINATION' be arranged so that all S's are together?

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