We analyze the spectrum and mixing among neutrinos in the minimal supersymmetric standard model with explicit breaking of [ital R] parity. It is shown that (i) the mixing among neutrinos could be large and (ii) the nonzero neutrino mass is constrained to be [le]10[sup [minus]5] eV from arguments based on baryogenesis. Thus vacuum oscillations of neutrinos in this model may offer a solution of the solar neutrino problem. The allowed space of the supersymmetric parameters consistent with this solution is determined.