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Definition: The  binomial coefficient (Binomialkoeffizient) "n choose k" of two natural numbers n and k:

(n k) := if 0 <= k <= n then n!/k!*(n-k)! else 0.

Proposition: We have for every n and k with 0 <= k <= n

(n k) = (prodn-k+1 <= i <= n i)/(prod1 <= i <= k i).

Important notion in combinatorics (the math of "counting things").

Author: Wolfgang Schreiner
Last Modification: November 16, 1999

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