${\displaystyle \left(\genfrac{}{}{0px}{}{n}{n-k}\right)}\backslash displaystyle\backslash binom\{n\}\{n-k\}\backslash \backslash$

Benutze die Formel für Binomialkoeffizienten.

${\displaystyle =\frac{n!}{(n-k)!(n-(n-k))!}}\backslash displaystyle=\backslash frac\{n!\}\{\backslash left(n-k\backslash right)!\backslash left(n-\backslash left(n-k\backslash right)\backslash right)!\}\backslash \backslash$

${\displaystyle n-(n-k)=n-n+k=k}\backslash displaystyle\; n-(n-k)=n-n+k=k\backslash \backslash$

${\displaystyle =\frac{n!}{(n-k)!\cdot k!}=\frac{n!}{k!\cdot (n-k)!}}\backslash displaystyle=\backslash frac\{n!\}\{\backslash left(n-k\backslash right)!\backslash cdot\; k!\}=\backslash frac\{n!\}\{k!\backslash cdot\backslash left(n-k\backslash right)!\}\backslash \backslash$

Hier steht bereits die Formel für Binomialkoeffizienten.