Many applications involve formulations or mixtures where large numbers of components are possible to choose from, but a final composition with only a few components is sought. Finding suitable binary or ternary mixtures from all the permissible components often relies on simplex-lattice sampling in traditional design of experiments (DoE), which requires performing a large number of experiments even for just tens of permissible components. The effect rises very rapidly with increasing numbers of components and can readily become impractical. This paper proposes constructing a single model for a mixture containing all permissible components from just a modest number of experiments. Yet the model is capable of satisfactorily predicting the performance for full as well as all possible binary and ternary component mixtures. To achieve this goal, we utilize biased random sampling combined with high dimensional model representation (HDMR) to replace DoE simplex-lattice design. Compared with DoE, the required number of experiments is significantly reduced, especially when the number of permissible components is large. This study is illustrated with a solubility model for solvent mixture screening.