  There are two apparent puzzles connected with the two-body and three-body
doubly charmed baryonic B decays. First, earlier calculations based on QCD sum
rules or the diquark model predict $Br(\bar
B^0\to\Xi_c^+\bar\Lambda_c^-)\approx Br(\bar B^0\to\B_c\bar N)$, while
experimentally the former has a rate two orders of magnitude larger than the
latter. Second, a naive estimate of the branching ratio $10^{-9}$ for the
color-suppressed three-body decay $\bar B\to\Lambda_c^+\bar\Lambda_c^-K$, which
is highly suppressed by phase space, is too small by five to six orders of
magnitude compared to experiment. We show that the great suppression for the
$\Lambda_c^+\bar\Lambda_c^-K$ production can be alleviated provided that there
exists a narrow hidden charm bound state with a mass near the
$\Lambda_c\bar\Lambda_c$ threshold. This new state that couples strongly to the
charmed baryon pair can be searched for in B decays and in $p\bar p$ collisions
by studying the mass spectrum of $D^{(*)}\bar D^{(*)}$ or
$\Lambda_c\bar\Lambda_c$. The doubly charmful decay $\bar
B\to\Xi_c\bar\Lambda_c$ has a configuration more favorable than the singly
charmful one such as $\bar B^0\to\Lambda_c\bar p$ since no hard gluon is needed
to produce the energetic $\Xi_c\bar\Lambda_c$ pair in the former decay, while
two hard gluons are needed for the latter process. Assuming that a soft $q\bar
q$ quark pair is produced through the $\sigma$ and $\pi$ meson exchanges in the
configuration for $\bar B\to \Xi_c\bar\Lambda_c$, it is found that its
branching ratio is of order $10^{-3}$, in agreement with experiment.
