  We explicitly construct and study the statistics of flux vacua for type IIB
string theory on an orientifold of the Calabi-Yau hypersurface
$P^4_{[1,1,2,2,6]}$, parametrised by two relevant complex structure moduli. We
solve for these moduli and the dilaton field in terms of the set of integers
defining the 3-form fluxes and examine the distribution of vacua. We compare
our numerical results with the predictions of the Ashok-Douglas density $\det
(-R - \omega)$, finding good overall agreement in different regions of moduli
space. The number of vacua are found to scale with the distance in flux space.
Vacua cluster in the region close to the conifold singularity. Large
supersymmetry breaking is more generic but supersymmetric and hierarchical
supersymmetry breaking vacua can also be obtained. In particular, the small
superpotentials and large dilaton VEVs needed to obtain de Sitter space in a
controllable approximation are possible but not generic. We argue that in a
general flux compactification, the rank of the gauge group coming from D3
branes could be statistically preferred to be very small.
