2023 AIME I Problems/Problem 1

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Problem

Five men and nine women stand equally spaced around a circle in random order. The probability that every man stands diametrically opposite a woman is $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n.$

Solutions

191

Solution 2

Something else

See also

2023 AIME I (ProblemsAnswer KeyResources)
Preceded by
First Question
Followed by
Problem 2
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All AIME Problems and Solutions