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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

The word $$ASSASSINATION$$ has $$4S,3A,2I,2N,T,O,4S$$ are together.
This is considered as one block as $$1$$ letter
Now we have $$3A,2I,2N,4S,T,O$$
$$\Rightarrow \dfrac{10!}{3!2!2!}=\dfrac{10\times 9\times 8\times 7\times 6\times 5\times 4\times 3!}{3!2!2!}$$
$$=10\times 9\times 8\times 7\times 6\times 5=151200$$ways.

Mathematics

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