Vandermonde's Identity - Generalized Vandermonde's Identity

Generalized Vandermonde's Identity

If in the algebraic derivation above more than two polynomials are used, it results in the generalized Vandermonde's identity. For y + 1 polynomials:

$\sum_{k_1+\dots +k_y = 0}^x {n\choose k_1} {n\choose k_2} {n\choose k_3} \cdots {n \choose x - \sum_{j = 1}^y k_j } = { \left( y + 1 \right) n \choose x}.$

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