Problem: "How many distinguishable 11-letter 'words' can be formed using the letters in

MISSISSIPPI?"

Because "words" is in quotations, I interpret that to simply mean 11-letter permutations and not real language words.

While each permutation must contain 11 letters, only 4 of those are unique: M (exactly 1 occurrence), I (exactly 4 occurrences), S (exactly 4 occurrences), and P (exactly 2 occurrences).

11! cannot be the answer because that would produce many duplicate permutations (whereas the problem calls only fordistinguishableones). So the answer must be 11!-x where x is the number of duplicates.

Here I get stuck. Any help will be appreciated.