Go backward to Factorial
Go up to Top
Go forward to Motivation
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").