Forty teams play a tournament. Each team plays every other team just once. Each game result in a win for one team. If each team has a 50% chance of winning each game, the probability that at the end of the tournament, every team has won a different number of games is

Question : Forty teams play a tournament. Each team plays every other team just once. Each game result in a win for one team. If each team has a 50% chance of winning each game, the probability that at the end of the tournament, every team has won a different number of games is

(A) 1/780

(B) \dfrac{40!}{2^{780}}

(C) \dfrac{40!}{3^{780}}

(D) None of these

Answer : option (B)

solution :

Forty teams play a tournament. Each team plays every other team just once. Each game result in a win for
one team. If each team has a 50% chance of winning each game, the probability that at the end of the
tournament, every team has won a different number of games is
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