  \noindent We study the asymptotic behavior of a sum of independent and
identically distributed random variables conditioned by a sum of independent
and identically distributed integer-valued random variables. We prove a
Berry-Esseen bound in a general setting and a large deviation result when the
Laplace transform of the underlying distribution is not defined in a
neighborhood of zero. Then we present several combinatorial applications. In
particular, we prove a large deviation result for the model of hashing with
linear probing.
