Think of a set with m + n elements as composed of two
Chapter 9, Problem 16E(choose chapter or problem)
Problem 16E
Think of a set with m + n elements as composed of two parts, one with m elements and the other with n elements. Give a combinatorial argument to show that
where m and n are positive integers and r is an integer that is less than or equal to both m and n.
This identity gives rise to many useful additional identities involving the quantities Because Alexander Vander-monde published an influential article about it in 1772, it is generally called the Vander-monde convolution. However, it was known at least in the 1300s in China by Chu Shih-chieh.
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