We study color allowed bottom baryon to s-wave and p-wave charmed baryon non-leptonic decays in this work. The charmed baryons include spin-1/2 and spin-3/2 states. Explicitly, we consider Lambda(b) -> Lambda(()(c)*(,)**M-)(-), Xi(b) -> Xi(()(c)**M-)(-) and Omega(b) ->Omega(()(c)*(,)**M-)(-) decays with M = pi, K, rho, K*, a(1), D, D-s, D*, D-s*, Lambda(()(c)*(,)**()) =Lambda(c), Lambda(c)(2595), Lambda(c)(2625), Lambda(c)(2765), Lambda(c)(2940), Xi(()(c)**()) = Xi(c), Xi(c)(2790), Xi(c)(2815) and Omega(()(c)*(,)**()) = Omega(c), Omega(c)(2770), Omega(c)(3050), Omega(c)(3090), Omega(c)(3120). There are six types of transitions, namely, (i) B-b ((3) over bar (f), 1/2(+)) to B-c((3) over bar (f), 1/2(+)), (ii) B-b (6(f), 1/2(+)) to B-c(6(f), 1/2(+)), (iii) B-b (6(f), 1/2(+)) to B-c(6(f), 3/2(+)), (iv) B-b(6f, 1=2+) to B-c(6f, 3=2, (v) B-b((3) over bar (f), 1/2(+)) to B-c((3) over bar (f), 1/2, and (vi) B-b((3) over bar (f), 1/2(+)) to B-b(6f, 3/2 transitions. Types (i) to (iii) involve spin 1/2 and 3/2 s-wave charmed baryons, while types (iv) to (vi) involve spin 1/2 and 3/2 p-wave charmed baryons. The light diquarks are spectating in these transitions. The transition form factors are calculated in the light-front quark model approach. All of the form factors in the 1/2 -> 1/2 and 1/2 -> 3/2 transitions are extracted, and they are found to reasonably satisfy the relations obtained in the heavy quark limit, as we are using heavy but finite m(b) and m(c). Using naive factorization, decay rates and up-down asymmetries of the above modes are predicted and can be checked experimentally. The study on these decay modes may shed light on the quantum numbers of Lambda(c) (2765), Lambda(c)(2940), Omega(c)(3050), Omega(c)(3090) and Omega(c)(3120).