How many permutations can be made from the word assassin?

1 Answer
Alan P.
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#

Related questions
See all questions in Probability and Permutations
Impact of this question
10559 views around the world
You can reuse this answer
Creative Commons License