Question

In how many ways can the letters of the word $ASSASSINATION$ be arranged so that all the $S^{\prime }s$ are together?

Answer 1

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 $3A,2I,2N,4S,T,O$

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

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