A statistical model for a kind of dilute ferromagnetism is presented. In thie model, a sublattice is a mixture of magnetic ions and non-magnetic ions, and the other sublattice is occupied exclusively by magnetic ions. Assuming the Ising type exchange interaction between magnetic ions, some exact results for the system obtained. The Curie temperature decreases as the concentration of magnetic ions decreaces and reachs the absolute zero of temperature at a critical concentration. At concentrations higher than the critical value, the specific heat remains finite and has a cusp with vertical tangent at the Curie temperature. The critical concentrations for several types of lattices are also given.