તમામ $\mathrm{S}$ સાથે આવે તે રીતે $\mathrm{ASSASSINATION}$ શબ્દના મૂળાક્ષરોની ગોઠવણી કેટલા પ્રકારે કરી શકાય ?

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 $=\frac{10 !}{3 ! 2 ! 2 !}=151200$