  We give explicit estimates for the Stirling numbers of the second kind
$S(n,m)$. With a few exceptions, such estimates are asymptotically sharp. The
form of these estimates varies according to $m$ lying in the central or
non-central regions of $\{1,\ldots ,n\}$. In each case, we use a different
probabilistic representation of $S(n,m)$ in terms of well known random
variables to show the corresponding results.
