We construct a simple multicomponent lattice gas model in one dimension in which each site can either be empty or occupied by at most one particle of any one of D species. Particles interact with a nearest-neighbor interaction which depends on the species involved. This model is capable of reproducing the relations between factorial moments observed in high-energy scattering experiments for moderate values of D. The factorial moments of the negative binomial distribution can be obtained exactly in the limit as D becomes large, and two suitable prescriptions involving randomly drawn nearest-neighbor interactions are given. These results indicate the need for considerable care in any attempt to extract information regarding possible critical phenomena from empirical factorial moments.