  We consider a system of classical particles confined in a box
$\Lambda\subset\mathbb{R}^d$ with zero boundary conditions interacting via a
stable and regular pair potential. Based on the validity of the cluster
expansion for the canonical partition function in the high temperature - low
density regime we prove moderate and precise large deviations from the mean
value of the number of particles with respect to the grand-canonical Gibbs
measure. In this way we have a direct method of computing both the exponential
rate as well as the pre-factor and obtain explicit error terms. Estimates
comparing with the infinite volume versions of the above are also provided.
