  Using a field-theoretic approach, we derive the first few coefficients of the
exact low-density (``virial'') expansion of a binary mixture of positively and
negatively charged hard spheres (two-component hard-core plasma, TCPHC). Our
calculations are nonperturbative with respect to the diameters $d_+$ and $d_-$
and charge valences $q_+$ and $q_-$ of positive and negative ions.
Consequently, our closed-form expressions for the coefficients of the free
energy and activity can be used to treat dilute salt solutions, where typically
$d_+ \sim d_-$ and $q_+ \sim q_-$, as well as colloidal suspensions, where the
difference in size and valence between macroions and counterions can be very
large. We show how to map the TCPHC on a one-component hard-core plasma (OCPHC)
in the colloidal limit of large size and valence ratio, in which case the
counterions effectively form a neutralizing background. A sizable discrepancy
with the standard OCPHC with uniform, rigid background is detected, which can
be traced back to the fact that the counterions cannot penetrate the colloids.
For the case of electrolyte solutions, we show how to obtain the cationic and
anionic radii as independent parameters from experimental data for the activity
coefficient.
