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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Answer 1

The word ASSASSINATION has 13 letters, of which A

appears 3 times, S appears 4 times, I appears 2 times, N

appears 2 times and the rest are all different. Since all the

S’s are to occur together, we take them as a single object

(SSSS). This single object together with 9 remaining letters

become 10 objects (SSSS) AAA II NN TO which can be arranged in $\frac{10!}{3!2!2!}$

The four S’s can be arranged among themselves in

$\frac{4!}{4!}$=1 way

∴ The required number of ways =$\frac{10!}{3!2!2!}×1 = \frac{10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{(3 \times 2 \times 1) \times (2 \times 1) \times (2 \times 1)}$

= 151200