Question

The probability that four $S$'s come consecutively in the word 'MISSISSIPPI' is $k/165$.Find the value of $k$

Answer 1

The word has $1M,2P^{\prime }s,4I^{\prime }sand4S^{\prime }s$ $\Rightarrow$ Total different words that can be formed $=\frac{11!}{4!4!2!}$
If all $S^{\prime }s$ are together,then total possible outcomes$=\frac{8!}{4!2!}$
Hence, probability$=\frac{8!4!}{11!}=\frac{4\times 3\times 2}{11\times 10\times 9}=\frac{4}{165}\Rightarrow k=4$