# How many permutations can be made from the word assassin?

##### 1 Answer
Mar 23, 2015

Treat each of the $8$ letters of "assassin" as if they were unique (perhaps by thinking of them as being different colors).
There would be 8! ways of doing this.

Of those 8! ways there are 2! times too many ways as "legal" because of duplication of the "a" letter sequences and 4! times too many ways because of duplication of "s" letter sequences.

Therefore the correct number of permutations (assuming the "a" and "s" letters were not distinguishable among themselves) would be:
(8!)/((2!)(4!))

$= 840$