${\displaystyle \left(\genfrac{}{}{0px}{}{9}{2}\right)=\frac{9\cdot 8}{1\cdot 2}=36}\backslash displaystyle\backslash binom\{9\}\{2\}=\backslash frac\{9\; \backslash cdot\; 8\}\{1\; \backslash cdot\; 2\}=36$

${\displaystyle \left(\genfrac{}{}{0px}{}{6}{3}\right)=\frac{6\cdot 5\cdot 4}{1\cdot 2\cdot 3}=20}\backslash displaystyle\backslash binom\{6\}\{3\}=\backslash frac\{6\backslash cdot\; 5\; \backslash cdot\; 4\}\{1\; \backslash cdot\; 2\; \backslash cdot\; 3\}=20$

Um diese Rechnung einfach zu lösen, ist es sinnvoll die Eigenschaft

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

${\displaystyle \left(\genfrac{}{}{0px}{}{12}{10}\right)={\displaystyle \left(\genfrac{}{}{0px}{}{12}{12-10}\right)={\displaystyle \left(\genfrac{}{}{0px}{}{12}{2}\right)=\frac{12\cdot 11}{1\cdot 2}=66}}}\backslash displaystyle\backslash binom\{12\}\{10\}=\backslash displaystyle\backslash binom\{12\}\{12-10\}=\backslash displaystyle\backslash binom\{12\}\{2\}=\backslash frac\{12\; \backslash cdot\; 11\}\{1\; \backslash cdot\; 2\}=66$