The limitations of expanding the pressure of a binary mixture of hard spheres as a power series in the diameters of the spheres is investigated. It is shown that such an expansion cannot give the correct monodisperse virial coefficients, while fulfilling certain exact conditions for diameter ratios of zero and one. Imposing the correct virial coefficients is shown to be difficult, without making substantial changes in the functional form of the pressure equation, for a reasonable choice of high virial coefficients.