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    • ▾Combinatorics
      • •Stirling numbers
      • ▸Catalan numbers
        • •Counting Binary Ops (NRICH activity)
        • •Number of ways to triangulate a regular polygon
        • ▸Young tableau
          • •One Basket or Group Photo (NRICH activity)
      • •Combinatorial proof: Binomial theorem
      • •Double counting
      • •History of combinatorics
      • •Inclusion–exclusion principle
      • ▸Pigeonhole principle
        • •Picking socks in the dark
      • •Proving Vandermonde's identity
      • •Stars and bars
      • •Sum and product rules
      • •Sum of squares of binomial coefficients
      • •Bell numbers
     › Combinatorics

    Proving Vandermonde's identity

    For \(0 \le m \le k \le n\),  \(\displaystyle \binom{m + n}{k} = \sum_{j = 0}^k \binom{m}{j}\binom{n}{k - j}\)
    70223Discrete Mathematical Structures, Lecture 1.6: Combinatorial proofs
    Professor Macauley
    238Vandemonde's Identity
    Elliot Nicholson