Question

In how many distinct permutations of the letters of the word MISSISSIPPI do four I's not come together?

• A. 840
• B. 34560
• C. 33810
• D. 24680

Answer 1

The correct option is B

34560

In the given word MISSISSIPPI, I appears 4 times , S appears 4 times, P appears 2 times, and M appears just once.

Therefore, number of distinct permutations of the letters in the given word $=\frac{11!}{4\times 4\times 2}=34650$

There are 4I's in the given word. When they occur together, they will be treated as a single object for the time being. This single object together with the remaining 7 objects will account for 8 objects.

In these 8 objects, there are 4 Ss and 2 Ps which can be arranged in $=\frac{8!}{4\times 2}=840$

Thus, number of distinct permutations of the letters of MISSISSIPPI in which 4 I's do not come together = 34650 - 840 = 33810