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

(nk) :=if0 <=k<=nthenn!/k!*(n-k)!else0.

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

(nk) = (prod_{n-k+1 <= i <= n}i)/(prod_{1 <= i <= k}i).

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

Author: Wolfgang Schreiner

Last Modification: November 16, 1999