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We consider a system of $p$ components of bosons, each of which consists of$N_{1},N_{2},\dots,N_{p}$ particles, respectively. The bosons are in threedimensions with interactions via a generalized interaction potential whichincludes the Coulomb interaction. We set the initial condition to describe amixture condensate, i.e., a tensor product of factorized states. We show thatthe difference between the many-body Schr\"odinger evolution in the mean-fieldregime and the corresponding $p$-particle dynamics due to a system of Hartreeequation is $O(N^{-1})$ where $N=\sum_{q=1}^{p}N_{q}$.

Rate of convergence towards equations of Hartree type for mixture condensates with factorized initial data