We report measurements of B-meson decays into two- and three-body final states containing two charmed baryons using a sample of 230×106 Υ(4S)→BB¯¯¯ decays. We find significant signals in two modes, measuring branching fractions B(B−→Λ+cΛ¯¯¯−cK−)=(1.14±0.15±0.17±0.60)×10−3 and B(B−→Ξ0cΛ¯¯¯−c)×B(Ξ0c→Ξ−π+)=(2.08±0.65±0.29±0.54)×10−5, where the uncertainties are statistical, systematic, and from the branching fraction B(Λ+c→pK−π+), respectively. We also set upper limits at the 90% confidence level on two other modes: B(B¯¯¯0→Ξ+cΛ¯¯¯−c)×B(Ξ+c→Ξ−π+π+)<5.6×10−5 and B(B¯¯¯0→Λ+cΛ¯¯¯−cK¯¯¯0)<1.5×10−3. We observe structure centered at an invariant mass of 2.93  GeV/c2 in the Λ+cK− mass distribution of the decay B−→Λ+cΛ¯¯¯−cK−.