Conformational selection and induced fit are well-known contributors to ligand binding and allosteric effects in proteins. Molecular dynamics (MD) simulations now enable the theoretical study of protein-ligand binding in terms of ensembles of interconverting microstates and the population shifts characteristic of "dynamical allostery." Here we investigate protein-ligand binding and allostery based on a Markov state model (MSM) with states and rates obtained from all-atom MD simulations. As an exemplary case, we consider the single domain protein par-6 PDZ with and without ligand and allosteric effector. This is one of the smallest proteins in which allostery has been experimentally observed. In spite of the increased complexity intrinsic to a statistical ensemble perspective, we find that conformational selection and induced fit mechanisms can be readily identified in the analysis. In the nonallosteric pathway, MD-MSM shows that PDZ binds ligand via conformational selection. However, the allosteric pathway requires an activation step that involves a conformational change induced by the allosteric effector Cdc42. Once in the allosterically activated state, we find that ligand binding can proceed by conformational selection. Our MD-MSM model predicts that allostery in this and possibly other systems involves both induced fit and conformational selection, not just one or the other.