Chu-Vandermonde Identity/Examples

Examples of Use of Chu-Vandermonde Identity

$3$ from $4 + 5$

$\ds \binom 9 3 = \binom {4 + 5} 3 = \sum_{k \mathop = 0}^3 \binom 4 k \binom 5 {3 - k}$

$2$ from $e + \pi$

Let $r = e$, $s = \pi$ and $n = 2$

$\ds \binom {e + \pi} 2 = \sum_{k \mathop = 0}^2 \binom e k \binom \pi {2 - k}$