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Theoretical predictions are presented for the production of two J=c -mesons, of a J=c -meson in association with an open charm hadron, and of two open charm hadrons from two c " c pairs in the LHC conditions. Processes in both single-and double-parton scattering mechanisms are taken into consideration. Special attention is paid to the kinematic limits of the LHCb detector, for which comparison with the newest experimental data is carried out.