Question

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

Answer 1

Given work is MISSISSIPPI, which has 11 letters of which M-1, S-4, I-4, P-2. 

∴ Total number of arrangements 

To find : Number of permutations of the letters in which four I’s not come together. 

First, we find number of permutations of the letters in which four I’s are kept together.

7 OTHER LETTERS

FOUR I'S

Now, we treat four P s together as single object this single object together with 7 remaining objects (letters) will account for 8 objects. These 8 objects in which there are four 5’s and two P’s 

can be arranged in   8!/4!2! ways. 

∴ Number of words in which I’s kept together.