This paper generalizes Moody's correlated binomial default distribution for homogeneous credit portfolio, which is introduced by Witt, to the case of inhomogeneous portfolios. As inhomogeneous portfolios, we consider two cases. In the first case, we treat a portfolio whose assets have uniform default correlation and non-uniform default probabilities. We obtain the default probability distribution and study the effect of the inhomogeneity on it. The second case corresponds to a portfolio with inhomogeneous default correlation. Assets are categorized in several different sectors and the inter-sector and intra-sector correlations are not the same. We construct the joint default probabilities and obtain the default probability distribution. We show that as the number of assets in each sector decreases, inter-sector correlation becomes more important than the intra-sector one. We study the maximum values of the inter-sector default correlation. In the modeling of portfolio credit risk, it is possible to incorporate realistic magnitude of inter-sector default correlations. We also show how to estimate the implied default correlation from the premium of tranches in CDO.