Factorial is considered the number of ways to arrange x distinct objects.
1! is 1 because there is 1 way to arrange 1 object. [1]
2! is 2 because there are 2 ways to arrange 2 objects (AB, BA). [2*1]
3! is 6 because there are 6 ways to arrange 3 objects (ABC, ACB, BAC, BCA, CAB, CBA) [3*2*1]
^So on and so forth.
So, 0! is 1 because there is 1 way to arrange 0 objects (_).