In this paper, we use a data set on admissions and enrolments for entry into the medical school of the Universite de Montreal to test the hypothesis that the admission process is meritocratic and free from discrimination and arbitrary decisions. The paper analyses the difficulty of choosing among different categories of applicants in the context of entrance quotas pertaining to the level of higher education (college, university) from which one applies to medical school. We use a sequential probit model to show that the performance variables, as measured or observed by the admissions committee through a variety of tests, only partially explain the committee's decisions. The school did not admit all the best in terms of performance, and among the best admitted, almost one out of three did not enrol. We explore some socioeconomic determinants of admissions and enrolments, and suggest an alternative approach to the admissions procedure.