In the wake of exploring CP-violation in the decays of B and B c mesons, we perform the straightforward calculation of their nonleptonic decay rates within a relativistic quark model. We confirm that the decays B c ->D s D 0 and B c ->D s D 0 are well suited to extract the Cabibbo-Kobayashi-Maskawa angle γ through the amplitude relations because their decay widths are the same order of magnitude. In the b-c sector the decays B->DK and B c ->DD lead to squashed triangles which are therefore not so useful to determine the angle γ experimentally. We also determine the rates for other nonleptonic B c -decays and compare our results with the results of other studies.