The thermodynamic properties of ternary fluid mixtures of two hard spheres and a heteronuclear dumbbell have been studied for a range of densities, concentrations, and two different dumbbell elongations. Standard Monte Carlo simulations in an NPT ensemble have been performed to obtain very accurate data on the equation of state, and an extended NVT ensemble has been used to obtain the chemical potential up to very high densities by means of a modified particle insertion method. The simulation results are compared with those obtained from the approximate Boublik-Nezbeda and bonded-hard-sphere analytic equations of state. It is shown that both equations are essentially identical and systematically underestimate the compressibility factor, whereas the chemical potential results agree in most cases with the simulation data within experimental error.