We consider a binary mixture of hard colloidal spheres and nonadsorbing polymer coils. The polymers are regarded as effective spheres that interact with one another via a repulsive step-function pair potential and with colloids solely via excluded volume. The system is treated with a geometry-based density functional theory based on the exact zero-dimensional limit of the model. For bulk fluid phases, we calculate demixing binodals and find that with increasing strength of polymer-polymer interaction the coexisting colloidal liquid (vapor) phase becomes more concentrated (dilute) in polymer. In contrast to a simple mean-fieldlike perturbative density functional, our approach yields good agreement with an experimental demixing phase diagram. (C) 2003 American Institute of Physics.