Proof of $0! = 1$ I have been recently studying binomial theorem and in that we very frequently encounter factorials. But one queer thing which I found is $0!$. Even more queer is its value which is > $0! = 1$. I was told this fact and I accepted it(without any proof). But I am still confused about it. How can we prove that $0!= 1 $?

We can order $n$ elements in $n!$ ways. $0$ elements can be ordered in just one way. One can choose $k$ of $n$ elements in ${n \choose k} = \frac{n!}{k!(n-k)!}$ ways. Obviously, $$1 = {n\choose n} = \frac{n!}{n!\cdot 0!}\text{.}$$ Also, $0! = 1$ agrees with Euler's function $\Gamma$, for which $\Gamma(n) = (n-1)!$ holds.

These are not proves, but only good reasons why should $0!$ equal $1$.