Probability Question 351
Question: Forty teams play a tournament. Each team plays every other team just once. Each game results 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
Options:
A) $ 1/780 $
B) $ 40!/2^{780} $
C) $ 40!/3^{780} $
D) none of these
Show Answer
Answer:
Correct Answer: B
Solution:
Team totals must be 0, 1, 2,-39,
Let the teams be $ T_1T_2,…,T_{40}, $
so that $ T_1 $ loses to $ T_1 $ for $ i<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} $ .
BETA
