Question 53
If $f(n, k)$ is the number of ways to divide the set $\{1,2, \ldots, n\}$ into $k$ nonempty subsets and $m$ is a positive integer, find a formula for
$$
\sum_{k=1}^{n} f(n, k)\, m(m-1)(m-2) \cdots (m-k+1).
$$
$$
\sum_{k=1}^{n} f(n, k)\, m(m-1)(m-2) \cdots (m-k+1).
$$