AMC 12 2016b 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 \textbf{(B)}\ 665 \textbf{(C)}\ 945 \textbf{(D)}\ 1140 \textbf{(E)}\ 1330