Think of a set with m+n elements as composed of two parts,
Chapter 9, Problem 9.233(choose chapter or problem)
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 m+n r=m 0n r+m 1 n r 1++m rn 0, 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 identitiesinvolvingthequantitiesn k.BecauseAlexanderVandermonde published an inuential article about it in 1772, it is generally called the Vandermonde convolution. However, it was known at least in the 1300s in China by Chu Shih-chieh.
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