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.