Use question $33$ to give an alternative proof of Corollary $2$ in Section $6.3,$ which states that $\binom{n}{k} = \binom{n}{n−k} $ whenever $k$ is an integer with $0 \leq k \leq n.[$Hint: Consider the number of paths of the type described in question $33$ from $(0, 0)\: \text{to}\: (n − k, k)$ and from $(0, 0)\: \text{to}\:(k, n − k).]$
