This is College Physics Answers with Shaun Dychko. This hypothetical decay of a muon into an electron electron neutrino and a muon neutrino will not happen because electron family number is not conserved. On the left, we have an electron family number of 0 and on the right-hand side, we have positive 1 for this electron and positive 1 for this electron neutrino. And so because electron family number is not conserved, this decay is probably not possible lepton conservation is not an exact conservation sometimes there is violation of electron family number or muon family number and so on but it's very unusual. And so in general, we'll say that this is not a decay that's possible.
Is the decay $\mu^- \to e^- + \nu_e + \nu_\mu$ possible considering the appropriate conservation laws? State why or why not.
No, electron family number is not conserved. This decay is probably not possible.