  We calculate several differential distributions for the production of charm
and dijets. Both single-parton scattering (SPS) and double-parton scattering
(DPS) contributions are calculated in the $k_T$-factorization approach. The
Kimber-Martin-Ryskin unintegrated parton distributions are used in our
calculations. Relatively low cuts on jet transverse momenta are imposed to
enhance the double-parton scattering mechanism contribution. We find dominance
of the DPS contribution over the SPS one. We have found regions of the phase
space where the SPS contribution is negligible compared to the DPS
contribution. The distribution in transverse momentum of charm quark/antiquark
or charmed mesons can be used to observe transition from the dominance of DPS
at low transvsverse momenta to the dominance of SPS at large transverse
momenta. Very distinct azimuthal correlation patterns (for $c \bar{c}$,
$c\mathrm{\textit{-jet}}$, $\mathrm{\textit{jet-jet}}$,
$D^0\mathrm{\textit{-jet}}$, $D^0 D^0$) are predicted as a result of the
competition of the SPS and DPS mechanisms.
