By integrating out the degrees of freedom of the small spheres in a bi
nary mixture of large and small hard spheres, we derive an explicit ef
fective Hamiltonian for the large spheres. Using the two-body (depleti
on potential) contribution to this effective Hamiltonian in simulation
s, we find stable fluid-solid and both metastable fluid-fluid and soli
d-solid coexistence in a mixture with size ratio q = 0.1. For q = 0.05
the solid-solid coexistence becomes stable.