How many permutations can be made from the word assassin?

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.
(8!)/((2!)(4!))
$= 840$