Difference between revisions of "1996 AIME Problems/Problem 6"
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== Problem == | == Problem == | ||
| + | In a five-team tournament, each team plays one game with every other team. Each team has a <math>50\%</math> chance of winning any game it plays. (There are no ties.) Let <math>\dfrac{m}{n}</math> be the probability that the tournament will product neither an undefeated team nor a winless team, where <math>m</math> and <math>n</math> are relatively prime integers. Find <math>m+n</math>. | ||
== Solution == | == Solution == | ||
Revision as of 15:50, 24 September 2007
Problem
In a five-team tournament, each team plays one game with every other team. Each team has a 
chance of winning any game it plays. (There are no ties.) Let 
be the probability that the tournament will product neither an undefeated team nor a winless team, where 
and 
are relatively prime integers. Find 
.
