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Probability of Quadrilateral in a Circle

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January 11, 2009
probability

Problem Statement

Six points on a circle are given. Four of the chords joining pairs of the six points are selected at random. What is the probability that the four chords are the sides of a convex quadrilateral? <spanclass=′latex−bold′>(A)</span> 115<spanclass=′latex−bold′>(B)</span> 191<spanclass=′latex−bold′>(C)</span> 1273<spanclass=′latex−bold′>(D)</span> 1455<spanclass=′latex−bold′>(E)</span> 11365 <span class='latex-bold'>(A)</span>\ \frac{1}{15}\qquad <span class='latex-bold'>(B)</span>\ \frac{1}{91}\qquad <span class='latex-bold'>(C)</span>\ \frac{1}{273}\qquad <span class='latex-bold'>(D)</span>\ \frac{1}{455}\qquad <span class='latex-bold'>(E)</span>\ \frac{1}{1365}
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