1999 AIME Problem 13

Forty teams play a tournament in which every team plays every other team exactly once. No ties occur, and each team has a 50 \% chance of winning any game it plays. The probability that no two teams win the same number of games is m/n, where m_{} and n_{} are relatively prime positive integers. Find \log_2 n.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.