InterviewSolution
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InterviewSolution
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Forty team play a tournament. Each team plays every other team justonce. Each game results in a win for one team. If each team has a 50% chance of winning each game,the probability that he end of the tournament, every team has won a differentnumber of games is`1//780`b. `40 !//2^(780)`c. `40 !//2^(780)`d. none of theseA. `1//780`B. `40!//2^(780)`C. `36//.^(64)C_(3)`D. `98//.^(64)C_(3)` |
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Answer» Correct Answer - B Team totals must be 0, 1, 2, …., 39. Let the teams be `T_(1)T_(2),…, T_(40)`, so that `T_(i)` loses to `T_(j)` for `i lt j`. In other words, this order uniquely determines the result of every game. There are `40!` such orders and 780 games, so `2^(780)` possible outcomes for the games. Hence, the probability is `40!//2^(780)`. |
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