Question

How many permutation are there in the word mississippi?

Answer 1

{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