2006 AIME A Problems/Problem 10
Problem
Seven teams play a soccer tournament in which each team plays every other team exactly once. No ties occur, each team has a chance of winning each game it plays, and the outcomes of the games are independent. In each game, the winner is awarded a point and the loser gets 0 points. The total points are accumilated to decide the ranks of the teams. In the first game of the tournament, team
beats team
The probability that team
finishes with more points than team
is
where
and
are relatively prime positive integers. Find