= Solution
Only a $t$-channel <Z boson> connects the muon-<neutrino> line to the <electron> line. Its endpoints are the <weak neutral current> vertices $Z\nu_\mu\bar\nu_\mu$ and $Ze^-e^+$. A <W boson> couples $\nu_\mu$ to a muon, so it cannot produce an additional elastic charged-current diagram with external electrons. There is no photon-<neutrino> vertex, and a strictly massless Standard Model <neutrino> has no Higgs Yukawa vertex. \b[There is one diagram.]
\Image[/past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2015/iii/paper-47-neutrino-diagrams.png]
{title=All five tree-level weak diagrams for muon-neutrino, electron-neutrino, and electron-antineutrino scattering on electrons}
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