TITLE: Vandermonde's Identity: How to find a closed formula for the given summation
QUESTION [10 upvotes]: I've stumbled upon the following challenging question. Find a closed formula for the following summation $$ S(a,b,n) = \sum_{k=0}^n {a \choose k} {b \choose n-k}$$ for all possible parameters $a,b$.
Anyone happens to see how to solve this one?

REPLY [3 votes]: http://en.wikipedia.org/wiki/Vandermonde%27s_identity