  Theoretical predictions of cross sections and properties of the
$J/\psi$-meson production in association with an open charm hadron and
formation of two open charm hadrons from two $c\bar{c}$ pairs in the LHC
conditions are presented. Processes in both single and in double parton
scattering mechanisms are included 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.
