Combinatorial Proof
Vandermonde's identity also admits a more combinatorics-flavored double counting proof, as follows. Suppose a committee in the US Senate consists of m Democrats and n Republicans. In how many ways can a subcommittee of r members be formed? The answer is
The answer is also the sum over all possible values of k, of the number of subcommittees consisting of k Democrats and r − k Republicans:
Read more about this topic: Vandermonde's Identity
Famous quotes containing the word proof:
“Sculpture and painting are very justly called liberal arts; a lively and strong imagination, together with a just observation, being absolutely necessary to excel in either; which, in my opinion, is by no means the case of music, though called a liberal art, and now in Italy placed even above the other two—a proof of the decline of that country.”
—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)