That song, and the red cup prop was used in the movie "Pitch Perfect." The song is an old one, but it got updated by a couple singers having fun - here is a YouTube link to the original, http://www.youtube.com/watch?v=DWCOYJg9ps4 by Lulu and the Lampshades - they use maybe yogurt containers, but in the movie, the Anna Kendrick character uses the classic Red Solo cup, ubiquitous on college campuses everywhere!

I didn't watch the competition, but as soon as you said Big Red Cup I knew what song it probably was!