  The annihilation of the $B_c$ meson to leptons and inclusive light hadrons is
analyzed in the framework of nonrelativistic QCD (NRQCD) factorization. We find
that the decay mode, which escapes from the helicity suppression, contributes a
sizable fraction width. According to the analysis, the branching ratio due to
the contribution from the color-singlet component of the meson $B_c$ can be of
order (10^{-2}). We also estimate the contributions from the color-octet
components. With the velocity scaling rule of NRQCD, we find that the
color-octet contributions are sizable too, especially, in certain phase space
of the annihilation they are greater than (or comparative to) the color-singlet
component. A few observables relevant to the spectrum of charged lepton are
suggested, that may be used as measurements on the color-octet and
color-singlet components in the future $B_c$ experiments. A typical long
distance contribution in the annihilation is estimated too.
