Is it permissible for students residing in university housing (200 km from their hometown) for a period ranging between 5 and 20 days, to shorten and combine prayers?

The distance mentioned is considered a distance for qasr (shortening prayers), but if you intend to stay for four full days—meaning, not counting the day of entry and the day of departure—in the university accommodation, then you are not permitted to shorten or combine prayers, because you are considered a resident.