We study color allowed Lambda(b) -> Lambda M-(*,**)(c)-, Xi(b) -> Xi M-(**)(c)- and Omega(b) -> Omega(()(c)*()) M- decays with M=pi, K,rho, K*, D, D-s, D*, D-s*, a(1), Lambda((*,**))(c) = Lambda(c), Lambda(c)(2595), Lambda(c)(2765), Lambda(c)(2940), Xi(()(c)**()) = Xi(c), Xi(c)(2790) and Omega(()(c)*()) = Omega(c), Omega(c)(3090), in this work. There are three types of transitions, namely B-b((3) over bar (f), 1/2(+)) -> B-c((3) over bar (f), 1/2(+)), B-b(6(f), 1/2(+)) -> B-c(6(f), 1/2(+)) and B-b((3) over bar (f), 1/2(+)) -> B-c((3) over bar (f), 1/2(-)) transitions. The bottom baryon to charmed baryon form factors are calculated using the light-front quark model. Decay rates and up-down asymmetries are predicted using naive factorization and can be checked experimentally. We find that in B-b -> BcP decays, rates in B-b(6(f), 1/2(+)) -> B-c(6(f), 1/2(+)) [type (ii)] transition are smaller than those in B-b((3) over bar (f), 1/2(+)) -> B-c((3) over bar (f), 1/2(+)) [type (i)] transition, but similar to those in B-b((3) over bar (f), 1/2(+)) -> B-c((3) over bar (f), 1/2(-)) [type (iii)] transition, while in B-b -> BcV, B(c)A decays, rates in B-b(6(f), 1/2(+)) -> B-c(6(f), 1/2(-)) [type (ii)] transition are much smaller than those in B-b((3) over bar (f), 1/2(+)) -> B-c((3) over bar (f), 1/2(+)) [type (i)] transition and are also smaller than those in B-b((3) over bar (f), 1/2(+)) -> B-c((3) over bar (f), 1/2(-)) [type (iii)] transition. For the up-down asymmetries, the signs are mostly negative, except for those in the B-b(6(f), 1/2(+)) -> B-c(6(f), 1/2(+)) [type (ii)] transition. All of these asymmetries are large in sizes. The study on these decay modes may shed light on the quantum numbers of some of the charmed baryons as the decays depend on the bottom baryon to charmed baryon form factors, which are sensitive to the configurations of the final state charmed baryons.