  In this note we apply mathematical results for the volume of certain
symmetric spaces to the problem of counting flux vacua in simple IIB
Calabi--Yau compactifications. In particular we obtain estimates for the number
of flux vacua including the geometric factor related to the Calabi-Yau moduli
space, in the large flux limit, for the FHSV model and some closely related
models. We see that these geometric factors give rise to contributions to the
counting formula that are typically not of order one and might potentially
affect the counting qualitatively in some cases. We also note, for simple
families of Calabi-Yau moduli spaces, an interesting dependence of the moduli
space volumes on the dimension of the flux space, which in turn is governed by
the Betti numbers of the Calabi-Yaus.
