We study the doubly charmful two-body and three-body baryonic B decays $\bar B\to \Lambda_c^+\bar \Lambda_c^-$ and $\bar B\to \Lambda_c^+\bar \Lambda_c^- \bar K$. As pointed out before, a naive estimate of the branching ratio ${\cal O}(10^{-8})$ for the latter decay is too small by three to four orders of magnitude compared to experiment. Previously, it has been shown that a large enhancement for the $\Lambda_c^+\bar\Lambda_c^-\bar K$ production can occur due to a charmonium-like resonance (e.g. X(4630) discovered by Belle) with a mass near the $\Lambda_c\bar\Lambda_c$ threshold. Motivated by the BaBar's observation of a resonance in the $\Lambda_c \bar K$ system with a mass of order 2930 MeV, we study in this work the contribution to $\bar B\to\Lambda_c^+\bar\Lambda_c^-\bar K$ from the intermediate state $\Xi_c(2980)$ which is postulated to be a first positive-parity excited $D$-wave charmed baryon state. Assuming that a soft $q\bar q$ quark pair is produced through the $\sigma$ and $\pi$ meson exchanges in the configuration for $\bar B\to \Xi_c(2980)\bar\Lambda_c$ and $\Lambda_c\bar\Lambda_c$, it is found that branching ratios of $\bar B\to \Lambda_c^+\bar \Lambda_c^- \bar K$ and $\bar B\to \Lambda_c^+\bar \Lambda_c^-$ are of order $3.5\times 10^{-4}$ and $5\times 10^{-5}$, respectively, in agreement with experiment except that the prediction for the $\Lambda_c\bar\Lambda_c K^-$ is slightly smaller. In conjunction with our previous analysis, we conclude that the enormously large rate of $\bar B\to \Lambda_c^+\bar \Lambda_c^-\bar K$ arises from the resonances $\Xi_c(2980)$ and X(4630).

Comment: 16 pages, 3 figures, 3 tables, version to appear in PRD