1996 AIME Problems/Problem 6

Revision as of 15:00, 24 September 2007 by 1=2 (talk | contribs) (Solution)

Problem

In a five-team tournament, each team plays one game with every other team. Each team has a $50\%$ chance of winning any game it plays. (There are no ties.) Let $\dfrac{m}{n}$ be the probability that the tournament will product neither an undefeated team nor a winless team, where $m$ and $n$ are relatively prime integers. Find $m+n$.

Solution

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See also

1996 AIME (ProblemsAnswer KeyResources)
Preceded by
Problem 5
Followed by
Problem 7
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All AIME Problems and Solutions