Chu-Vandermonde Identity/Proof 3

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Theorem

$\displaystyle \sum_k \binom r k \binom s {n - k} = \binom {r + s} n$


Informal Proof

The right hand side can be thought of as the number of ways to select $n$ people from among $r$ men and $s$ women.

Each term in the left hand side is the number of ways to choose $k$ of the men and $n - k$ of the women.

$\blacksquare$


Source of Name

This entry was named for Alexandre-Théophile Vandermonde and Chu Shih-Chieh.


Sources