  The discovery of $\Xi_{cc}^{++}$ has inspired new interest in studying doubly
heavy baryons. In this study, the weak decays of a doubly charmed baryon ${\cal
B}_{cc}$ to a light baryon ${\cal B}$ and a charm meson $D^{(*)}$ (either a
pseudoscalar or a vector one) are calculated. Following our previous work, we
calculate the short distance contributions under the factorization hypothesis,
whereas the long distance contributions are modeled as the final state
interactions which are calculated with the one particle exchange model. We find
that the ${\cal B}_{cc}\to {\cal B} D^{*}$ decays' branching ratios are
obviously larger, as they receive contributions of more polarization states.
Among the decays that we investigate, the following have the largest branching
fractions: ${\cal BR}(\Xi_{cc}^{++}\rightarrow\Sigma^{+}D^{*+}) \in [0.46\%,
3.33\%]$ estimated with $\tau_{\Xi_{cc}^{++}}=256$ fs; ${\cal
BR}(\Xi_{cc}^{+}\rightarrow\Lambda D^{*+}) \in [0.38\%, 2.63\%]$ and ${\cal
BR}(\Xi_{cc}^{+}\rightarrow\Sigma^{0} D^{*+}) \in [0.45\%, 3.16\%]$ with
$\tau_{\Xi_{cc}^+}=45$ fs; and ${\cal BR}(\Omega_{cc}^{+}\rightarrow\Xi^{0}
D^{*+}) \in [0.27\%, 1.03\%]$, ${\cal BR}(\Omega_{cc}^{+}\rightarrow\Xi^{0}
D^{+}) \in [0.07\%, 0.44\%]$ and ${\cal
BR}(\Omega_{cc}^{+}\rightarrow\Sigma^{0} D^{*+}) \in [0.06\%, 0.45\%]$ with
$\tau_{\Omega_{cc}^+}=75$ fs. By comparing the decay widths of pure color
commensurate channels with those of pure bow-tie ones, we find that the bow-tie
mechanism plays an important role in charm decays.
