Binomial Coefficient is Integer/Proof 1

Proof
If it is not the case that $0 \le k \le n$, then the result holds trivially.

So let $0 \le k \le n$.

By the definition of binomial coefficients:

The numerator is a product of $k$ successive integers.

From Factorial Divides Product of Successive Numbers, $k!$ divides it.