  We consider a general class of disordered mean-field models where both the
spin variables and disorder variables take finitely many values. To investigate
the size-dependence in the phase-transition regime we construct the metastate
describing the probabilities to find a large system close to a particular
convex combination of the pure infinite-volume states. We show that, under a
non-degeneracy assumption, only pure states are seen, with non-random
probability weights for which we derive explicit expressions in terms of
interactions and distributions of the disorder variables. We provide a
geometric construction distinguishing invisible states (having zero weights)
from visible ones. As a further consequence we show that, in the case where
precisely two pure states are available, these must necessarily occur with the
same weight, even if the model has no obvious symmetry relating the two.
