Correlations reduce the configurational entropies of liquids below their ideal gas limits. By means of first-principles molecular dynamics simulations, we obtain accurate pair correlation functions of liquid metals, then subtract the mutual information content of these correlations from the ideal gas entropies to predict the absolute entropies over a broad range of temperatures. We apply this method to liquid aluminum and copper and demonstrate good agreement with experimental measurements; then, we apply it to predict the entropy of a liquid aluminum copper alloy. Corrections due to electronic entropy and many-body correlations are discussed.