  We investigate higher dimensional cosmological models in the semiclassical
approximation with Hartle-Hawking Boundary conditions, assuming a gravitational
action which is described by the scalar curvature with a cosmological constant.
In the framework the probability for quantum creation of an inflationary
universe with a pair of black holes in a multidimensional universe is
evaluated. The probability for creation of a universe with a spatial section
with $S^{1}XS^{D -2}$ topology is then compared with that of a higher
dimensional de Sitter universe with $S^{D -1}$ spatial topology. It is found
that a higher dimensional universe with a product space with primordial black
holes pair is less probable to nucleate when the extra dimensions scale factors
do not vary in an inflating universe.
