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In how many ways can the letters of the word $\mathrm{ASSASSINATION} $ be arranged so that all the $\mathrm{S}$ 's are together?
$151200$
$151200$
$151200$
$151200$
Solution
In the given word $ASSASSINATION$, the letter $A$ appears $3$ times, $S$ appears $4$ times, $I$ appears $2$ times, $N$ appears $2$ times, and all the other letters appear only once. since all the words have to be arranged in such a way that all the $Ss$ are together, $SSSS$ is treated as a single object for the time being. This single object together with the remaining $9$ objects will account for $10$ objects.
These $10$ objects in which there are $3 \,As , 2$ $Is$, and $2 \,Ns$ can be arranged in $\frac{10 !}{3 ! 2 ! 2 !}$ ways.
Thus, Required number of ways of arranging the letters of the given word $=\frac{10 !}{3 ! 2 ! 2 !}=151200$
