Summary and Contributions: This paper studies the selection problem, which (in the most general case) can be stated as follows: there is a data-independent set of n candidate solutions R that we would like to select from. For each candidate r in R, there is a quality score function q_r that maps any input dataset D to a real number q_r(D). The goal is to, given dataset D, select r in R that maximizes q_r(D), while respecting the notion of differential privacy (DP). Here, we say that the algorithm incurs an error of q * - Expectation[q_{output}(D)] where q * min_r q_r(D); in other words, the error is the expected quality loss of the return solution compared to the optimum. Many well-studied problems in machine learning can be stated in the selection formulation; for example, each r could be a hypothesis and q_r(D) is the empirical error.