Chu-Vandermonde Identity/Examples/3 from 4 + 5/Proof 1

Example of Use of Chu-Vandermonde Identity

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

Proof

From the Chu-Vandermonde Identity:

$\ds \sum_{k \mathop = 0}^n \binom r k \binom s {n - k} = \binom {r + s} n$

The result follows on setting $r = 4$, $s = 5$ and $n = 3$.

$\blacksquare$