Why does $\binom{n}{k} = 0$, if $k > n$? I have came across this in a textbook that I am currently studying, but I don't understand how I should proof this.
A short explanation or proof would be nice.

For example expand the binomial
$$
(1+x)^n
$$
and the coefficient of $x^k$ is $\binom{n}{k}$ for all $k$.  [This is why it is called a binomial coefficient.]  Of course (when $n$ is a positive integer), this coefficient is $0$ for $k > n$.
