We present a quantitative model to describe the formation of hydrogen atoms (1s and 2p states) following the dissociation of fast (30--120 keV/u) hydrogen cluster ions ${\mathrm{H}}_{\mathrm{n}}^{+}$ (n=2 and n= 3 -- 21, odd) induced by a thin carbon foil. The model includes Coulomb explosion, multiple scattering, energy loss, and a simplified description of charge-exchange processes inside the solid. This description takes into account the dynamic screening of the moving protons by the target electrons and the relative position of the protons during the charge-exchange process. The results of the calculations performed with a Monte Carlo computer code reproduce remarkably well the experimental data.