In how many ways can the letters of the word | vedclass

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(A) In the word $ASSASSINATION$,the total letters are $13$. The frequency of letters is: $A: 3, S: 4, I: 2, N: 2, T: 1, O: 1$.To keep all $4$ $S$'s to

Vedclass · Accepted Answer

$151200$

Vedclass · Answer

(A) In the word $ASSASSINATION$,the total letters are $13$. The frequency of letters is: $A: 3, S: 4, I: 2, N: 2, T: 1, O: 1$.To keep all $4$ $S$'s together,we treat the block $(SSSS)$ as a single unit.Now,we have $9$ remaining letters plus the $1$ unit of $(SSSS)$,totaling $10$ objects.These $10$ objects consist of $3$ $A$'s,$2$ $I$'s,and $2$ $N$'s.The number of arrangements is given by the formula $\frac{10!}{3!2!2!}$.Calculating this: $\frac{3628800}{6 	imes 2 	imes 2} = \frac{3628800}{24} = 151200$.

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

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