می‌دانيم $\left( _{r}^{n} \right)=\left( _{n-r}^{n} \right)$، بنابراین: \[\left( _{n}^{21} \right)=\left( _{3n-3}^{21} \right)\Rightarrow n+3n-3=21\Rightarrow 4n=24\Rightarrow n=6\]