TITLE: How would I figure out how many anagrams of mississippi don't contain the word psi?
QUESTION [11 upvotes]: I'm really confused how I'd calculate this. I know it's the number of permutations of mississippi minus the number of permutations that contain psi, but considering there's repetitions of those letters, I'm not sure how I'd do it.

REPLY [3 votes]: The simplest solution is very similar to user29743's.  The trick to counting permutations containing a given number of copies of "PSI" is to treat each "PSI" as a single symbol.  We want
(# of permutations of MISSISSIPPI) - (# of permutations of [PSI]SSSIIIMP) + (# of permutations of [PSI][PSI]SSIIM)
$$= {11\choose 4,4,2,1} - {9\choose 3,3,1,1,1} + {7\choose2,2,2,1} = 25200.$$