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Theoretical predictions of cross sections and properties of the$J/\psi$-meson production in association with an open charm hadron andformation of two open charm hadrons from two $c\bar{c}$ pairs in the LHCconditions are presented. Processes in both single and in double partonscattering mechanisms are included into consideration. Special attention ispaid to the kinematic limits of the LHCb detector for which comparison with thenewest experimental data is carried out.

Associated production of $J/\psi$-mesons and open charm and double open charm production at the LHC