${\displaystyle {}k>n}$

${\displaystyle {}{\binom {n}{k}}=0\neq k\,.}$

${\displaystyle {}1}$

${\displaystyle {}n\geq 1}$

${\displaystyle {}{\binom {n}{1}}=n\,}$

und dies gilt auch für ${\displaystyle {}n=0}$.

${\displaystyle {}{\binom {\binom {3}{2}}{1}}={\binom {3}{1}}=3\,}$

und

${\displaystyle {}{\binom {3}{\binom {2}{1}}}={\binom {3}{2}}=3\,.}$

${\displaystyle {}{\binom {\binom {4}{3}}{2}}={\binom {4}{2}}=6\,,}$

aber

${\displaystyle {}{\binom {4}{\binom {3}{2}}}={\binom {4}{3}}=4\,.}$