If a hyperbolic 3-manifold M admits a reducible and a finite Dehn filling,
the distance between the filling slopes is known to be 1. This has been proved
recently by Boyer, Gordon and Zhang. The first example of a manifold with two
such fillings was given by Boyer and Zhang. In this paper, we give examples of
hyperbolic manifolds admitting a reducible Dehn filling and a finite Dehn
filling of every type: cyclic, dihedral, tetrahedral, octahedral and
icosahedral.