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Question
In how many ways can the letters of the word ASSASSINATION be arranged so that all the S’s are together?
Solution
There are total 13 letters in ASSASSINATION, in which A is used three times, S four times, I twice and N twice. 4 – S have to live together. Therefore, it was considered a letter. Thus, 10 letters remain in it in which 3 – A, 2 – 1 and 2 – N are the same.
∴ The arrangement of letters of this word when S remains together
= `(10)/(322)`
= `(10 xx 9 xx 8 xx 7 xx 6 xx 5 xx 4 xx 3 xx 2 xx 1)/((3 xx 2 xx 1)xx(2 xx 1) xx (2 xx 1))`
= 151200
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