A basic sampling problem with applications in many domains asks the number of r.v. from a given distribution needed such that an output can be selected to be distributed according to another distribution. A covering problem motivated by non-asymptotic information theory and formulated by Verdu lower bounds the probability that at least one r.v. falls in a set. We observe a simple min-max duality between the two problems, and discuss two applications in achievability of sampling (both hard to solve directly by constructing explicit samplers without appealing to covering lemmas and duality): First, the moment of the number of samples is characterized by a Renyi divergence. Second, the error exponent in sampling a joint distribution is characterized using a sharp mutual covering lemma.