We study the semileptonic decays B c → B n ℓ + ν ℓ where B c(n) is the anti-triplet-charmed (octet) baryon with the SU (3) f flavor symmetry and helicity formalism. In particular, we present the decay branching ratios of B c → B n ℓ + ν ℓ in three scenarios: (a) an exact SU (3) f symmetry with equal masses for the anti-triplet-charmed (octet) baryon states of B c (B n ), (b) SU (3) f parameters without the baryonic momentum-transfer dependence, and (c) SU (3) f with baryonic transition form factors in the heavy quark limit. We show that our results are all consistent with the existing data. Explicitly, we predict that B(Ξ + c → Ξ 0 e + ν e ) = (11.9 ± 1.3, 9.8 ± 1.1, 10.7 ± 0.9) × 10 −2 and B(Ξ 0 c → Ξ − e + ν e ) = (3.0 ± 0.3, 2.4 ± 0.3, 2.7 ± 0.2) × 10 −2 in the scenarios (a), (b) and (c) agree with the data of (14.0 +8.3 −8.7 ) × 10 −2 and (5.6 ± 2.6) × 10 −2 from the CLEO Collaboration, respectively. In addition, we obtain that B(Λ + c → ne + ν e ) = (2.8 ± 0.4, 4.9 ± 0.4, 5.1 ± 0.4) × 10 −3 in (a), (b) and (c).We also examine the longitudinal asymmetry parameters of α(B c → B n ℓ + ν ℓ ), which are sensitive to the different scenarios with SU (3) f . Some of the decay branching ratios and asymmetries can be observed by the ongoing experiments at BESIII and LHCb as well as the future searches by BELLEII.