This illustrates the proof that $\left(\begin{matrix}n\\k\end{matrix}\right)=\left(\begin{matrix}n\\n-k\end{matrix}\right)$ in the case $\left(\begin{matrix}7\\3\end{matrix}\right)=\left(\begin{matrix}7\\4\end{matrix}\right)$. The picture shows the subsets $A\subseteq\{1,\dotsc,7\}$ with $|A|=3$ in green, and the subsets $B$ with $|B|=4$ in blue. Each set is paired with its complement, showing that the number of $A$'s is the same as the number of $B$'s. The number of $A$'s is $\left(\begin{matrix}7\\3\end{matrix}\right)$ and the number of $B$'s is $\left(\begin{matrix}7\\4\end{matrix}\right)$.