  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 three
dimensions with interactions via a generalized interaction potential which
includes the Coulomb interaction. We set the initial condition to describe a
mixture condensate, i.e., a tensor product of factorized states. We show that
the difference between the many-body Schr\"odinger evolution in the mean-field
regime and the corresponding $p$-particle dynamics due to a system of Hartree
equation is $O(N^{-1})$ where $N=\sum_{q=1}^{p}N_{q}$.
