2010 Pascal Problem 25

Six soccer teams are competing in a tournament in Waterloo. Every team is to play three games, each against a different team. (Note that not every pair of teams plays a game together.) Judene is in charge of pairing up the teams to create a schedule of games that will be played. Ignoring the order and times of the games, how many different schedules are possible?

\textbf{(A)}\ 90\quad \textbf{(B)}\ 100\quad \textbf{(C)}\ 80\quad \textbf{(D)}\ 60\quad \textbf{(E)}\ 70

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Pascal contests here.