Explaining why an event occurred involves solving different information-processing problems: inferring what actually happened (causal inference) but also highlighting which of the causes contributed most significantly to the outcome (causal selection). While much research has investigated causal inference and causal selection separately, little has studied them jointly. We report results of an experiment (N=215) examining how these aspects of causal reasoning interact, as is the case in real-world explanation settings. We study explanations in scenarios where the states of some variables are unobserved and may be partially or completely inferrable from the outcome, and we also vary the variables' rarity or rates of occurrence. Using a computational model, we show that participants engage in both inference and selection: they infer the state of unobserved variables on the basis of available evidence, and exhibit behavioral signatures of causal selection. Specifically they select the rarer cause when both are needed for the effect to occur, and the less rare cause when either is sufficient. Overall, we capture the qualitative patterns in participant selections across a wide range of explanation scenarios with a suite of model variants, suggesting people balance a variety of considerations when providing explanations under uncertainty.