Question

If the letters of the word MISSISSIPPI are arranged at random, the probability that all the 4S's appear consecutively is

• A. $\frac{8!}{11!}$
• B. $\frac{4!}{11!}$
• C. $\frac{8!4!}{11!}$
• D. $\frac{6!}{11!}$

Answer 1

Answer: (C)

$\frac{8!4!}{11!}$

No. of arrangements with all $S$'s together = $\frac{8!}{4!\ast 2!}$
Total no. of arrangements = $\frac{11!}{4!\ast 4!\ast 2!}$
Hence, required probability = $\frac{\frac{8!}{4!\ast 2!}}{\frac{11!}{4!\ast 4!\ast 2!}}=\frac{8!\ast 4!}{11!}$