Basically, x!, or "X Factorial", asks "Given x items, how many unique orders can they have, if put in a line?"
So, 2! = 2, AB or BA.
3! = 6, ABC ACB BAC BCA CAB CBA
1! is trivial, A.
How many arrangements can 0 objects have? One unique arrangement, in fact: ∅
Also,
4!/3! = 4
3!/2! = 3
2!/1! = 2
And we all know how mathematicians love patterns.
1!/0! = 1
Therefore, 1! = 0!