  We consider the production of charmed baryons and mesons in the
proton-antiproton binary reactions at the energies of the future $\bar{P}$ANDA
experiment. To describe these processes in terms of hadronic interaction
models, one needs strong couplings of the initial nucleons with the
intermediate and final charmed hadrons. Similar couplings enter the models of
binary reactions with strange hadrons. For both charmed and strange hadrons we
employ the strong couplings and their ratios calculated from QCD light-cone sum
rules. In this method finite masses of $c$ and $s$ quarks are taken into
account. Employing the Kaidalov's quark-gluon string model with Regge poles and
adjusting the normalization of the amplitudes in this model to the calculated
strong couplings, we estimate the production cross section of charmed hadrons.
For $p\bar{p}\to \Lambda_c\bar{\Lambda}_c$ it can reach several tens of $nb$ at
$p_{lab}= 15 {GeV}$, whereas the cross sections of $\Sigma_c$ and $D$ pair
production are predicted to be smaller.
