  Baryons with a heavy c-quark or a heavy b-quark and also two c-quarks have
been discovered. These states are expected in QCD and therefore provide a test
for the theory. There should be double beauty baryons, and also an intriguing
possibility that baryons ${\bf B}_{bc}$ with a c-quark, a b-quark. These states
are yet to be discovered. The main decay modes of ${\bf B}_{bc}$ are expected
to be weak processes from theoretical understanding of their mass spectrum.
These decay modes can provide crucial information about these heavy baryons
${\bf B}_{bc}$. We analyze two body hadronic weak decays for ${\bf B}_{bc}$
using $SU(3)$ flavor symmetry. Any one of the $c$ and $b$ decays will induce
${\bf B}_{bc}$ to decay. We find that the Cabibbo allowed decays ${\bf B}_{bc}
\to {\bf B}_b + M$ due to $c \to s u \bar d$ can be crucial for exploration.
The LHC may have the sensitivity to discover such decays. Other ${\bf B}_{bc}$
decays due to $b \to c q' \bar q$ are sub-leading. Several relations among
branching ratios are obtained which can be used to test $SU(3)$ flavor
symmetry.
