How many permutation are there in the word mississippi?
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{M1,I4,S4,P2}
There are only four Is in “Mississippi” so you want to count permutations of letters where the Is are not all together.
The total number of permutations is
11!/1!4!4!2!
Treating the four Is as a single block we can count the permutations where they are all together, we essentially count the permutations of the 8 objects M,{IIII}, S,S,S,S,P,P to give
8!/1!1!4!2!
the number of desired permutations is the difference between these
11!/1!4!4!2!−8!/1!1!4!2!=33810
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