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We say that a quadrilateral is a bow-tie if two of the sides cross each other. Seven different points are chosen on a circle. We draw all C(7,2) chords that connect two of these points. Four of these 21 chords are selected at random. What is the probability that the four chords form a bow-tie quadrilateral?

 Jan 31, 2020
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The probability is 5/399.

 Jan 31, 2020

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