We report on the inclusive branching fractions of B- and of B0bar mesons decaying to D0 X, Dbar0 X, D+ X, D- X, Ds+ X, Ds- X, Lambdac+ X, Lambdabarc- X, based on a sample of 88.9 million BBbar events recorded with the BABAR detector at the Upsilon(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 anti-charmed particles per B decay and derive the total charm yield per B- decay, n_c- = 1.313 +/- 0.037 +/- 0.062 {+0.063}{-0.042}, and per Bbar0 decay, n_c0 = 1.276 +/- 0.062 +/- 0.058 {+0.066}{-0.046} where the first uncertainty is statistical, the second is systematic, and the third reflects the charm branching-fraction uncertainties.