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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?
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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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