We consider the Falicov-Kimball model in the case of an equal number of classical “nuclei” and quantum “electrons” with Fermi statistics. In one dimension we find an exact formula for the leading behavior of the ground-state energy as a function of the attractive potential U between electrons and nuclei. For U > U_c the system forms “atoms” which have an effective repulsion between them. Similar results hold for a continuum model provided there is a sufficiently large hard core between the nuclei. Some low-temperature properties are also discussed.