We report on a study of inclusive $B^-$ and $\bar{B}^0$ meson decays to ${D^0 X}$, ${\bar{D}^0 X}$, ${D^+ X}$, ${D^- X}$, ${D_s^+ X}$, ${D_s^- X}$, ${\Lambda_c^+ X}$, ${\bar{\Lambda}_c^- X}$, based on a sample of 231 million $B\bar{B}$ events recorded with the BABAR detector at the $\Upsilon{(4S)}$ resonance. Events are selected by completely reconstructing one $B$ and searching for a reconstructed charm particle in the rest of the event. From the measured branching fractions of these decays, we infer the number of charm and anti-charm particles per $\bar{B}$ decay, separately for charged and neutral parents. We derive the total charm yield per $B^-$ decay, $n_c^- = 1.202 \pm 0.023\pm 0.040^{+0.035}_{-0.029} $, and per $\bar{B}^0$ decay, $n_c^0 = 1.193 \pm 0.030\pm 0.034^{+0.044}_{-0.035}$ where the first uncertainty is statistical, the second is systematic, and the third reflects the charm branching-fraction uncertainties. We also present the charm momentum distributions measured in the $\bar{B}$ rest frame.