The Gemara on 74b asks "If there are nine Yisraelim and one Nochri, what
is the law? It answers that we learn from a Gezeirah Shavah "Toch-Toch" that there must be ten Jews.
what was special about 9-1? Either we need 10 Yisraelim or 9 and metzaref
the Shchina--but where does a single eino-Yehudi come into play?
aurel littmann, brooklyn,ny
The ARUCH LA'NER writes that the Gemara originally thought that the requirement of ten people was based on logical grounds only. Therefore, although we surely need Yisraelim, perhaps a non-Jew could be the tenth man (since most of the group are Yisraelim). The Gemara concludes that we learn that ten people are considered "b'Farhesya" from a Pasuk, and therefore all ten must be Yisraelim.
The Sedei Chemed (Ma'arechet Gimel #67, referenced by the Margoliyus ha'Yam) explains that the Halachah is that a convert can be among the 10 because there are two Mi'utim for Gerim (Benei Yisrael and b' Soch), and "Ein Mi'ut Achar Mi'ut Ela Lerabos." I propose that Rebbi Yirmeyah's Hava Amina was that both of the Mi'utim exclude Nochrim , and because "Ein Mi'ut Achar Mi'ut Ela Lerabos" we should include a Nochri in the Halachah.
(According to this answer, though, the question should have been about ten Nochrim, and not just nine Jews and one Nochri. M. Kornfeld)