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 
