Exercise 11.
Let \(k_1, k_2, \ldots, k_j\) be a list of positive integers that sum to \(n\) (i.e., \(\sum_{i=1}^j k_i = n\)). Use two graphs containing \(n\) vertices to explain why
\begin{equation*}
\sum_{i = 1}^j \binom{k_i}{2} \le \binom{n}{2}\text{.}
\end{equation*}