Chiew’s equation of state for mixtures of hard-sphere chains is generalized through the Carnahan-Starling radial distribution function for hard-sphere mixtures at contact for both the bonding and nonbonding terms. When compared with computer simulations of hard-sphere-chain mixtures, the new equation of state gives better agreement than the original equation of state. The new equation of State indicates the simplifying physical assumptions which are required to obtain the well-known Flory-Huggins athermal entropy of mixing. The generalization presented here is applied to mixtures of hard-sphere-chain copolymers, where the spherical segments of a given chain may have different diameters. Illustrative calculations are presented for three types of copolymers (alternating, block, and random).