Question

How many different words can be formed with the letters of the word 'MISSISSIPPI'?

Answer 1

There are 11 letters in the given word, of which 4 are S's, 4 are I's and 2 are P's. So, total number of words is the number of arrangements of 11 things, of which 4 are similar of one kind, 4 are similar of second kind and 2 are similar of third kind is $=\frac{11!}{4!4!2!}$
Hence; the total number of words $=\frac{11!}{4!4!2!}=34650$