The Bekenstein-Hawking formula for the entropy of black holes implies a large degeneracy of microstates. Starting from the work of Strominger-Vafa, we now have large families of examples of extremal (supersymmetric) blackholes where we have an understanding of the microstates. Such counting has been typically done in superstring theories with large $\mathcal{N}\geq 4$ supersymmetry with the generating function being an automorphic form. The extension of this counting to superstring theories with $N=2$ supersymmetry is not as well developed. We would like to study the microscopic counting of degeneracies of $\mathcal{N}=2$ supersymmetric black holes considering type IIA string theory compactified on Calabi-Yau threefolds. Our focus is on a particular family of Calabi-Yau threefolds that appear as the Z_2 orbifolds of K3 X T2 -- these are called the Borcea-Voisin manifolds. The generating function of degeneracy of electrically charged black holes in these theories is given by a (generic) product formula due to Gopakumar-Vafa. One of our initial goals is to determine the precise version of this product formula. Eventually, we would like to determine formulae for the generating function of the degeneracy of dyonic black holes and match the results with the Bekenstein-Hawking entropy.