Question: Explain in words why the equation left(begin{array}{c}n kend{array} ight) = left(begin{array}{c}n n-kend{array} ight)is true. Use the definitionleft(begin{array}{c}n kend{array} ight) = frac{n!}{k!(n-k)!}to show that the equation

  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.

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