From the thermodynamic viewpoint the glass transition is a second-order change: there is no latent heat involved, so the entropy varies continuously through the transition. But the transition is not a reversible process. A simulation study of the hard-sphere fluid shows that the statistical entropy, defined in terms of the configuration integral, decreases by 0·20 ± 0·03Nkwhen it forms a glass, which indicates that a system ofNhard spheres can form about exp (0·2N) glasses. For the system ofN= 256 spheres studied there are about 1022distinct glasses.