Question

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

Answer 1

The word MISSISSIPPI has one M, four I’s, four S’s, two P’s and a total of 11 letters.

The number of all type of arrangements possible with the given alphabets

Let us first find the case when all the I’s together and so take it as one packet or unit. So now we have one M, one unit of four I’s, four S’s, two P’s and a total of 8 units.

Therefore the number of arrangements possible when all the I’s is together

Hence, the distinct permutations of the letters of the word MISSISSIPPI when four I’s do not come together = 34650 – 840 = 33810.