Difference between revisions of "1999 AIME Problems/Problem 13"
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== Problem == | == Problem == | ||
| + | Forty teams play a tournament in which every team plays every other team exactly once. No ties occur, and each team has a <math>\displaystyle 50 \%</math> chance of winning any game it plays. The probability that no two teams win the same number of games is <math>\displaystyle m/n,</math> where <math>\displaystyle m_{}</math> and <math>\displaystyle n_{}</math> are relatively prime positive integers. Find <math>\displaystyle \log_2 n.</math> | ||
== Solution == | == Solution == | ||
== See also == | == See also == | ||
| + | * [[1999_AIME_Problems/Problem_12|Previous Problem]] | ||
| + | * [[1999_AIME_Problems/Problem_14|Next Problem]] | ||
* [[1999 AIME Problems]] | * [[1999 AIME Problems]] | ||
Revision as of 02:07, 22 January 2007
Problem
Forty teams play a tournament in which every team plays every other team exactly once. No ties occur, and each team has a 
chance of winning any game it plays. The probability that no two teams win the same number of games is 
where 
and 
are relatively prime positive integers. Find 
