  We derive an approximate analytic relation between the number of consistent
heterotic Calabi-Yau compactifications of string theory with the exact charged
matter content of the standard model of particle physics and the topological
data of the internal manifold: the former scaling exponentially with the number
of Kahler parameters. This is done by an estimate of the number of solutions to
a set of Diophantine equations representing constraints satisfied by any
consistent heterotic string vacuum with three chiral massless families, and has
been computationally checked to hold for complete intersection Calabi-Yau
threefolds (CICYs) with up to seven Kahler parameters. When extrapolated to the
entire CICY list, the relation gives about 10^23 string theory standard models;
for the class of Calabi-Yau hypersurfaces in toric varieties, it gives about
10^723 standard models.
