Mathematics Simplified
Wednesday, September 21, 2011
Combinatorial proofs
Prove the following using combinational proofs (i.e not using the formulas)
C(n, k) = C(n - 1, k) + C(n - 1, k - 1)
C(n, k) = C(n - 1, k) + C(n - 1, k - 1)
C(n, k) = C(n, n - k).
C(n, r)C(r, k) = C(n, k)C(n-k, r-k)
k·C(n, k) = n·C(n - 1, k - 1)
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