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| − | == Problem ==
| + | #REDIRECT [[2006 AIME I Problems/Problem 10]] |
| − | Seven teams play a soccer tournament in which each team plays every other team exactly once. No ties occur, each team has a <math> 50\% </math> 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 <math> A </math> beats team <math> B. </math> The probability that team <math> A </math> finishes with more points than team <math> B </math> is <math> m/n, </math> where <math> m </math> and <math> n </math> are relatively prime positive integers. Find <math> m+n. </math>
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| − | == Solution ==
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| − | {{solution}}
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| − | == See also ==
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| − | *[[2006 AIME II Problems/Problem 9 | Previous problem]]
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| − | *[[2006 AIME II Problems/Problem 11 | Next problem]]
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| − | *[[2006 AIME II Problems]]
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| − | [[Category:Intermediate Combinatorics Problems]]
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