Count the number of ways to choose a leader, a deputy leader, and a team from $n$ people in two different ways.
As before, we have two possibilities: choose the chief and then the deputy chief first, or choose the team containing the chief and deputy chief first. We
obtain the identity

$$
\sum_{k=0}^{n} k(k-1)\binom{n}{k}=n(n-1) 2^{n-2}
$$