Combinatorial chemistry techniques provide a promising route to the design of macromolecules that acquire predetermined folded conformations. A library of sequences based on a pool of different monomer types dan be synthesized, where the sequences are partially designed so as to be consistent with a particular target conformation. The library is screened for folding molecules. The number of sequences grows rapidly with the length of the polymer, however, and both the experimental and computational tabulation of sequences become infeasible. For polymers and libraries of arbitrary size; we present a self-consistent, mean-field theory that can be used to estimate the number of sequences as a function of the energy in a target structure. The theory also yields the probabilities that each position in the sequence is occupied by a particular monomer type. The theory is tested using a simple lattice model of proteins, and excellent agreement between the theory and the results of exact enumerations are observed. The theory may be used to quantify particular design strategies and the facility of finding low-energy sequences for particular structures. The theory is discussed with an eye toward protein design and the mutability of particular residues in known proteins.