Q11Written answer
In how many words can the letters of the word ASSASSINATION be arranged so that all the S’s are together?
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Worked solution
Ans: 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 the time being. This single 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 = $\dfrac{{10!}}{{2!3!2!}}\, = \,15120$.