“red Solo cup” means nothing here. actually, i don’t think you can even buy them (at least not the true Solo brand). you can imagine my surprise as a 20-something graduate student.
some light reading on the cup’s history if you’ve never experienced the American “party staple”: http://slate.me/qT45ON
side note: most bars don’t offer mixed drinks. you get beer, wine, or a shot. the only way to get a mixed drink is to do it yourself (order a shot of Jack and buy a coke)