Mo logo [home] [lexicon] [problems] [tests] [courses] [auxiliaries] [notes] [staff] german flag
Mathematics-Online lexicon:

Binomial Coefficient

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z overview

For $ n,k \in{\mathbb{N}}_0$ with $ n \geq k$ the binomial coefficient $ \binom{n}{k} $ is defined as

$\displaystyle \binom{n}{k} = \frac{n!}{(n-k)!k!} = \frac{n(n-1)(n-2)\cdots(n-k+1)}{1 \cdots (k-2)(k-1)k}\,. $

With $ 0! = 1$ we have in particular

$\displaystyle \left(\begin{array}{c}0 \\ 0\end{array} \right) = 1, \quad \left... ...\ n\end{array} \right) = \left(\begin{array}{c}n \\ 0\end{array}\right) = 1 . $

The binomial coefficient $ \binom{n}{k} $ equals the number of $ k$-subsets of a set containing $ n$ elements.

(Authors: Kimmerle/Abele)

Example:

[Links]
  automatically generated 6/11/2007