2016 AMC 12B Problem 20

A set of teams held a round-robin tournament in which every team played every other team exactly once. Every team won 10 games and lost 10 games; there were no ties. How many sets of three teams \{A, B, C\} were there in which A beat B, B beat C, and C beat A?

\textbf{(A)}\ 385 \qquad \textbf{(B)}\ 665 \qquad \textbf{(C)}\ 945 \qquad \textbf{(D)}\ 1140 \qquad \textbf{(E)}\ 1330

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.