This paper presents an econometric technique for circumventing the lack of individual choice data in a framework of binary choice model by utilizing aggregate choice data. The probability of observing a certain number of individuals making choice A out of the total number of individuals in a group is presented as a sum of probabilities of disjoint events, in which some individuals are picked to make choice A, and others are not. These probabilities are then used to form a likelihood function. The model, which is estimated using the method of maximum likelihood, performs favorably in an application to real discrete choice data.