Measurement of the branching fractions for inclusive $B^{-}$ and ${\overline{B}}^0$ decays to flavor-tagged $D$, $D_s$, and ${\Lambda }_c$

We report on the inclusive branching fractions of $B^{-}$ and of ${\overline{B}}^0$ mesons decaying to $D^{0}X$, ${\overline{D}}^{0}X$, $D^{+}X$, $D^{-}X$, $D_s^{+}X$, $D_s^{-}X$, ${\Lambda }_c^{+}X$, ${\overline{\Lambda }}_c^{-}X$, based on a sample of $88.9\times {10}^6$ $B\overline{B}$ events recorded with the BABAR detector at the ${\rm Y}(4S)$ resonance. Events are selected by completely reconstructing one $B$ and searching for a reconstructed charmed particle in the rest of the event. We measure the number of charmed and of anticharmed particles per $B$ decay and derive the total charm yield per $B^{-}$ decay $n_c^{-}=1.313\pm 0.037\pm {0.062}_{-0.042}^{+0.063}$ and per ${\overline{B}}^0$ decay $n_c^0=1.276\pm 0.062\pm {0.058}_{-0.046}^{+0.066}$, where the first uncertainty is statistical, the second is systematic, and the third reflects the charm branching-fraction uncertainties.