A method to efficiently simulate diffusion and reaction in a single-file system is presented. By considering all possible configurations of M species in a length N one-dimensional pore, a deterministic model consisting of (M+1)(N) variables can be constructed for the system. The order of the system can then be significantly reduced by considering only pairs of adjacent cells, or (M+1)(2)(N-1) doublets. This lumped model is able to capture the most important correlations between cells when the dominant mode of transport is through single-site hops. Extensions of this method for higher dimensional pores and more complex molecular interactions are discussed. The results of the approximation are compared to results of the full deterministic model, and new situations are investigated. The implications of single-file behavior are discussed for reversible reactions and molecules of different mobilities.