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

Question

Philoid · Accepted Answer

Total number of letters in MISSISSIPPI =11

Letter Number of occurrence

⇒ Number of permutations =

We take that 4 I’s come together, and they are treated as 1 letter,

∴ Total number of letters=11-4+1=8

⇒ Number of permutations =

Therefore, total number of permutations where four I’s don’t come together = 34650-840=33810