How do you find $0!$

Question

I have been taking math and going through various forms of factorials for the purposes of probability, but I have not been able to find a conclusive reason as to how one accounts for 0! I am not sure if there is a way to solve it?

Answer 1

There is only one permutation of zero objects.

Answer 2

Work recursively:

$$3!=\frac{4!}{4}=\frac{24}{4}=6$$ $$2!=\frac{3!}{3}=\frac 63 =2$$ $$1!=\frac{2!}{2}=\frac 22 =1$$ $$0!=\frac{1!}{1}=\frac 11=1$$