If all the letters of the word MISSISSIPPI ar | vedclass

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Question

(B) The word $MISSISSIPPI$ has $11$ letters,consisting of $4$ $S$,$4$ $I$,$2$ $P$,and $1$ $M$.The total number of arrangements is $\frac{11!}{4!4!2!1!

Vedclass · Accepted Answer

$4/165$

Vedclass · Answer

(B) The word $MISSISSIPPI$ has $11$ letters,consisting of $4$ $S$,$4$ $I$,$2$ $P$,and $1$ $M$.The total number of arrangements is $\frac{11!}{4!4!2!1!} = \frac{39916800}{24 	imes 24 	imes 2} = 34650$.To find the number of arrangements where all $4$ $S$ come together,treat the block $(SSSS)$ as a single unit.Now we have $8$ units to arrange: $(SSSS), I, I, I, I, P, P, M$.The number of arrangements of these $8$ units is $\frac{8!}{4!2!1!} = \frac{40320}{24 	imes 2} = 840$.The probability is $\frac{840}{34650} = \frac{84}{3465} = \frac{4}{165}$.

If all the letters of the word $MISSISSIPPI$ are rearranged,what is the probability that all $S$ come together?

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