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

$\begin{array}{1 1}(A)\;151200\\(B)\;152200\\(C)\;153200\\(D)\;154200\end{array}$

Toolbox:
• $n!=n(n-1)(n-2)(n-3).......(3)(2)(1)$
• $C[(n,r)]=\large\frac{n!}{r!(n-r)!}$
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
$\Rightarrow \large\frac{10!}{3!2!2!}=\frac{10\times 9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}{(3\times 2\times 1)\times (2\times 1)\times (2\times 1)}$
$\Rightarrow 10\times 9\times 8\times 7\times 5\times 3\times 2$
$\Rightarrow 151200$
Hence (A) is the correct answer.