The magnetic behaviors of the Fe-Mn-Al alloy are simulated on the Bethe lattice by using a trimodal random bilinear exchange interaction (J) distribution in the Blume-Capel (BC) model. Ferromagnetic (J > 0) or antiferromagnetic (J < 0) bonds or dilution of the bonds (J = 0) are assumed between the atoms with some probabilities. It is found that the second-or the first-order phase boundaries separate the ferromagnetic (F), antiferromagnetic (AF), paramagnetic (P), or spin-glass (SG) phases from the possible other one. In addition to the tricritical points, the special points at which the second-and the first-order and the spin-glass phase lines meet are also found. Very rich phase diagrams in agreement with the literature are obtained.