Question

The letters of the word $MISSISSIPI$ are arranged in a row at random. Then the probability that all $S$ come together is

• A. $\frac{4}{35}$
• B. $\frac{5}{28}$
• C. $\frac{1}{7}$
• D. $\frac{1}{30}$

Answer 1

The correct option is D $\frac{1}{30}$

There are total $7$ letters and among which there are $4$ $S$

So no of with all $S$ together are $\frac{7!}{4!}$

And total arrangements will be $\frac{10!}{4!4!}$

Probability that all $S$ together $=\frac{7!/4!}{10!/4!4!}=\frac{4\times 3\times 2}{10\times 9\times 8}=\frac{1}{30}$