Properties and decays of the $B_c$ meson and $b$ baryons

Using the large data sample collected by the CERN LHCb experiment, we present studies of $B_c$ mesons and $b$ baryons, including the first observation of new decay modes of the $B_c$ meson as well as high precision mass measurements. The polarization amplitudes in $\Lambda_b \to J/\psi \Lambda_0$ decay are measured together with measurements of the transverse polarisation of $\Lambda_b$ baryons produced in $\sqrt{s}$=7 TeV $pp$ collisions