  In many statistical multifragmentation models the volume available to the $N$
nonoverlapping fragments forming a given partition is a basic ingredient
serving to the simplification of the density of states formula. One therefore
needs accurate techniques for calculating this quantity. While the direct
Monte-Carlo procedure consisting of randomly generating the fragments into the
freeze-out volume and counting the events with no overlapped fragments is
numerically affordable only for partitions with small $N$, the present paper
proposes a Metropolis - type simulation which allows accurate evaluations of
the free volume even for cases with large $N$. This procedure is used for
calculating the available volume for various situations. Though globally this
quantity has an exponential dependence on $N$, variations of orders of
magnitude for partitions with the same $N$ may be identified. A parametrization
based on the virial approximation adjusted with a calibration function,
describing very well the variations of the free volume for different partitions
having the same $N$ is proposed. This parametrization was successfully tested
within the microcanonical multifragmentation model from [Al. H. Raduta and Ad.
R. Raduta, Phys. Rev. C {\bf 55}, 1344 (1997); {\it ibid.}, {\bf 56}, 2059
(1997)]. Finally, it is proven that parametrizations of the free volume solely
dependent on $N$ are rather inadequate for multifragmentation studies producing
important deviations from the exact results.
