We have developed a novel computational scheme that allows direct numerical simulation of polymer-colloid mixtures at constant osmotic pressure. Using this technique, we have studied the entropic attraction that is caused by ideal polymers dissolved in a simple (hard-sphere) colloidal dispersion. In particular, we studied the nonpairwise additivity of the polymer-induced entropic interaction. The present simulations show that the nonpairwise additivity has a pronounced effect on the structure of a polymer-colloid mixture.