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We investigate the weak decays of (B) over bar (0)(s) and Lambda(b) to charm hadrons based on the dynamical supersymmetry between the (s) over bar quark and the ud diquark. We derive a new sum rule relating the decay rates of the processes (B) over bar (0)(s) -> Ds+P-, (B) over bar (0)(s) -> Ds*+P-, and Lambda(b) -> Lambda P-c(-) where P- is a negatively charged meson, such as pi(-) and K-. It is found that the observed decay rates satisfy the sum rule very well. This implies that the supersymmetry between the (s) over bar quark and the ud diquark is also seen in the wave functions of the heavy hadrons and suggests that the ud diquark can be regarded as a valid effective constituent for heavy hadrons.