We report a computer-simulation study of a simple model for a colloid dispersed in a polymer solution. The simulations were performed using a computational scheme that allows simulation at constant osmotic pressure of the polymers. We present results for the polymer-induced interaction, the equation-of-state, and the phase diagram. The simulations show that when the radius of gyration of the polymers R(g) is sufficiently large compared to the diameter of the colloidal particles sigma(col) (2R(g)/sigma(col)greater than or equal to 0.45), addition of polymer induces a colloidal "liquid-vapor" phase separation. For shorter polymers, only the solid-fluid transition is observed. In addition, we find that the nonpairwise additivity of the polymer-induced attraction between the colloidal particles has a pronounced effect on the equation-of-state and the phase behavior of a colloid-polymer mixture. The perturbation theory of Lekkerkerker et al. [Europhys. Lett. 20, 559 (1992)] is found to perform well, except at low densities.