Symmetry Rule for Binomial Coefficients/Proof 1

Proof
Follows directly from the definition of binomial coefficient, as follows.

If $k < 0$ then $n - k > n$.

Similarly, if $k > n$, then $n - k < 0$.

In both cases:
 * $\dbinom n k = \dbinom n {n - k} = 0$

Let $0 \le k \le n$.