A generalized Vandermonde

#Vandermonde#generalization#identity

Statement

Prove $\sum_{k=0}^n\binom{m}{k}\binom{p}{n-k}=\binom{m+p}{n}$ .

Hint

Same as Vandermonde's identity.

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See "Vandermonde's identity" in this category.

Conclusion. The generalized Vandermonde holds for all nonnegative $m,p,n$ .