Question

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

Answer 1

There are 13 letters in the word 'ASSASSINATION' out of which 3 are A's, 4 are S's, 2 are 1's, 2 are N's and the rest are all distinct.

Considering all S's together and treating them as one letter we have 10 letters.

These 10 letters can be arranged in $\frac{10!}{3!2!2!}$

= $\frac{10\times 9\times 8\times 7\times 6\times 5\times 4\times 3!}{3!\times 2\times 2}$

= $10\times 9\times 8\times 7\times 6\times 5$

=151200.

Hence, the total words are 151200.