Wording of question is a little strange - let me explain:
take 8 as X
X! = 40320
and that's the possibilities of an 8-character string, like 'abcdefgh'. Does this number include possibilities of say 'abc' and 'dse' or is it strict to using all 8 characters?
If we have $8$ distinct things, we can arrange them in a variety of ways. We have $8$ choices for the first thing, then since we have used one, we have only $7$ choices for the second thing, $6$ for the third, etc. So we have $8\times 7\times 6\times 5\times 4\times 3\times 2\times 1$ ways to arrange the $8$ things. This is called "$8$ factorial", and denoted $8!$.
If we want to make only arrangements of $3$ things from our set of $8$ different things. There are $8\times 7\times 6$ ways. Do you see why?
If, for example, $3$ of our $8$ objects are identical, then there will be $8!/3!$ ways to arrange the $8$ objects in different ways. Do you see why here as well?