This paper addresses the problem of clustering binary data with feature selection within the context of maximum likelihood (ML) and classification maximum likelihood (CML) approaches. In order to efficiently perform the clustering with feature selection, we propose the use of an appropriate Bernoulli model. We derive two algorithms: Expectation-Maximization (EM) and Classification EM (CEM) with feature selection. Without requiring a knowledge of the number of clusters, both algorithms optimize two approximations of the minimum message length (MML) criterion. To exploit the advantages of EM for clustering and of CEM for fast convergence, we combine the two algorithms. With Monte Carlo simulations and by varying parameters of the model, we rigorously validate the approach. We also illustrate our contribution using real datasets commonly used in document clustering.