The magnetic and transport properties of Mn-doped ZnO thin films codoped with Sn are examined. Superconducting quantum interference device magnetometry measurements indicate that the films are ferromagnetic with an inverse correlation between magnetization and electron density as controlled by Sn doping. Magnetism in low free-electron density material is consistent with the bound magnetic polaron model, in which bound acceptors mediate the ferromagnetic ordering. Increasing the electron density decreases the acceptor concentration, thus quenching the ferromagnetic exchange. This result is important in understanding ferromagnetism in transition-metal-doped semiconductors for spintronic devices.