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Difference between revisions of "2016 AMC 10B Problems/Problem 22"

(Created page with "==Problem== A set of teams held a round-robin tournament in which every team played every other team exactly once. Every team won <math>10</math> games and lost <math>10</mat...")
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Revision as of 09:31, 21 February 2016

Problem

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 $A?$

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

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