The Monte Carlo method was used to determine the compression factors and radial distribution functions (rdf) of ternary hard-sphere mixtures with hard-sphere diameters sigma(A) = 1, sigma(B) = 0.6, sigma(C) = 0.3 at several packing fractions (gamma = 0.35, 0.40 and 0.45) and mole fractions (x(A) = x(B) = x(C) = 1/3 or x(A) = 1/6, x(B) = 1/3, x(C) = 1/2). The obtained values of the compression factor were employed to test the equations of state of hard-sphere mixtures. Fair agreement was found in all the cases. Also the obtained contact values of rdf s, g(ij)(sigma(ij)), compare well with the theoretical values. Simulation results for the dependence of the rdf's on distance were compared with values determined from a simple relation devised recently for calculation of g(ij)((x) over bar) in ternary and multi-component systems. In all the cases, a satisfactory agreement was found for distances close to the contact values. Larger deviations were found in the range of distances close to the first minimum of g(ij). The magnitude of deviations increases with the increasing differences between sigma(ij) and sigma(A). In the case of considerably different values of sigma(ij) and sigma(A), the proposed theoretical method overestimates g(ij) for (x) over bar greater than or equal to (x) over bar(min).