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

Asked by Abhisek | 1 year ago |  172

##### Solution :-

There are 3 A’s, 4 S’s, 2 I’s and all other letters appear only once in the word ASSASSINATION. The given word should be arranged such that all the S’s are together.
The 4 S’s can be treated as a single object for time being. This ingle object with the remaining objects will be 10 objects together. These 10 objects with 3 A’s, 2 I’s and 2 N’s can be arranged in $$\dfrac{10!}{2!3!2!}$$ ways.

Therefore, number of ways of arranging the given word

$$\dfrac{10!}{2!3!2!}$$ = 15120



Answered by Pragya Singh | 1 year ago

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