Weak decays of bottom-charm baryons: $$\mathcal {B}_{bc}\rightarrow \mathcal {B}_bP$$ <math> <mrow> <msub> <mi>B</mi> <mrow> <mi>bc</mi> </mrow> </msub> <mo>→</mo> <msub> <mi>B</mi> <mi>b</mi> </msub> <mi>P</mi> </mrow> </math>

After the discovery of the double-charm baryon $$\Xi _{cc}^{++}$$ Ξ cc + + by LHCb, one of the most important topics is to search for the bottom-charm baryons which contain a b quark, a c quark and a light quark. In this work, we study the two-body non-leptonic weak decays of a bottom-charm baryon into a spin-1/2 bottomed baryon and a light pseudoscalar meson with the short-distance contributions calculated under the factorization hypothesis and the long-distance contributions considering the final-state-interaction effects. The branching fractions of all fifty-seven decay channels are estimated. The results indicate that $$\Xi _{bc}^+\rightarrow \Xi _b^0\pi ^+$$ Ξ bc + → Ξ b 0 π + , $$\Xi _{bc}^{0}\rightarrow \Xi _{b}^{-}\pi ^+$$ Ξ bc 0 → Ξ b - π + and $$\Omega _{bc}^0\rightarrow \Omega _b^-\pi ^+$$ Ω bc 0 → Ω b - π + decay modes have relatively large decay rates and thus could be used to experimentally search for the bottom-charm baryons. The topological diagrams and the SU(3) symmetry of bottom-charm baryon decays are discussed.