We analyze the effects of costs, geographical accessibility, and quality of higher education institutions on participation and on the composition of enrolled students, in terms of their educational and socioeconomic backgrounds. We develop a theoretical framework for higher education choices of secondary school graduates where differently talented individuals are financially constrained both in the participation decision and in the choice of which university to attend. The predictions of our theoretical model are tested by estimating a nested logit model for the enrollment decision and university choice where the effect of supply-side attributes is allowed to be heterogeneous across students' secondary school backgrounds and family social classes. We find that lower costs and a greater geographical distribution increase enrollments by economically disadvantaged students and, at the same time, by students with weaker educational backgrounds. Instead, higher quality institutions attract more talented students regardless of their families' economic and social status.