1. Explain in words why the equation \left(\begin{array}{c}n\\ k\end{array} ight) = \left(\begin{array}{c}n\\ n-k\end{array} ight)is true.
2. Use the definition\left(\begin{array}{c}n\\ k\end{array} ight) = \frac{n!}{k!(n-k)!}to show that the equation in question (1) is true.