As far as I understand, nationalities in Japanese are expressed either using the name of the nation together with [人]{じん} to form an adjective, or directly using the name of the nation with the の particle. For example, to say "Chinese person", we can say either
中国[人]{じん}
or
中国の[人]{ひと}
I suppose the same holds for a generic term like 外国, which translates to "foreign country". So, I would either use 外国[人]{じん} or 外国の[人]{ひと}. I've found a sentence in my textbook, both written and spoken, which goes like:
この大学に外国[人]{じん}の先生が35[人]{にん}います。
So, is it incorrect to attach 外国 to 先生 (unlike it is for [人]{ひと}) saying
外国の先生
just like one says
外国の[人]{ひと}
or to use 中国[人]{じん} directly as an adjective (so without the particle の, that is 中国[人]{じん}先生). Probably English is leading me off track and this is not an adjective in Japanese (also, would it be a -い or -な adjective?), but even then I don't understand. Can you shed some light on this?
Incidentally, here's the audio. The sentence is at 0:37.