A maximum likelihood approach is developed for a pattern recognition problem where the patterns are described by configurations of simple easily recognized parts called primitives. The approach is capable of dealing with three types of noise: measurement noise in the location and shape of observed primitives, undetected or missing primitives (leakage), and the unexpected appearance of extra primitives (false alarms). The approach is called combinatorial because the likelihood function dictates that observed primitives must be assigned to known primitives in all possible combinations. Due to the complexity of the likelihood function, practical classifiers must be based on likelihood function approximations. Several are proposed, and most of these are simple enough to be used in a gradient search strategy for recognizing distorted patterns with random orientations. Examples are included to show the characteristics of combinatorial classifier performance.