Question

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

Answer 1

Here, total letters are 13 in the word ASSASSINATION in which A appears 3 times, S appears 4 times, I appears 2 times and N appears 2 times. Now four 'S's taken together become a single letter and other remaining letters taken with this single letter.

$\therefore$ Number of arrangements = $\frac{10!}{3!2!2!}=\frac{10\times 9\times 8\times 7\times 6\times 5\times 4\times 3!}{3!2\times 1\times 2\times 1}$

= $10\times 9\times 8\times 7\times 6\times 5=151200.$