Kategorie:Binomialkoeffizient

${\displaystyle \forall n,k\in \mathbb {N} ,k\leq n:\qquad {\binom {n}{k}}={\frac {n!}{k!(n-k)!}}}$

Äquivalente Definition (Merkregel): ${\displaystyle {\binom {n}{k}}={\frac {\overbrace {n\cdot (n-1)\cdot (n-2)\cdots (n-k+1)} ^{k\;{\text{Glieder}}}}{\underbrace {1\cdot 2\cdots k} _{k\;{\text{Glieder}}}}}}$ Spezialfall: ${\displaystyle {\tbinom {n}{0}}:=1}$