A versatile new approach for calculating the depletion potential in a hard-
sphere mixture is presented. This is valid for any number of components and
for arbitrary densities. We describe two different routes to the depletion
potential for the limit in which the density of one component goes to zero
. Both routes can be implemented within density functional theory and simul
ation. We illustrate the approach by calculating the depletion potential fo
r a big hard sphere in a fluid of small spheres near a planar hard wall. Th
e density functional results are in excellent agreement with simulations.