  We study the two-body and three-body charmful baryonic B decays: $\bar B^0\to
\Lambda_c\bar p$ and $\bar B\to \Lambda_c \bar p\pi(\rho)$. The factorizable
W-exchange contribution to $\bar B^0\to\Lambda_c\bar p$ is negligible. Applying
the bag model to evaluate the baryon-to-baryon weak transition matrix element,
we find $B(\bar B^0\to\Lambda_c\bar p)\leq 1.1\times
10^{-5}|g_{B^0p\Sigma_b^+}/6|^2$ with $g_{B^0p\Sigma_b^+}$ being a strong
coupling for the decay $\Sigma_b^+\to \bar B^0 p$ and hence the predicted
branching ratio is well below the current experimental limit. The factorizable
contributions to $B^-\to\Lambda_c\bar p\pi^-$ can account for the observed
branching ratio of order $6\times 10^{-4}$. The branching ratio of order
$2\times 10^{-3}$ for $B^-\to\Lambda_c\bar p\rho^-$ is larger than that of
$B^-\to\Lambda_c\bar p\pi^-$ by a factor of about 2.6. We explain why the
three-body charmful baryonic B decay has a larger rate than the two-body one,
contrary to the case of mesonic B decays.
