Question

How many permutations can be made from the word assassin?

Answer 1

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`