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We define a bow-tie quadrilateral as a quadrilateral where two sides cross each other. An example of a bow-tie quadrilateral is shown below.

 

 

Seven distinct points are chosen on a circle. We draw all \(\binom{7}{2} = 21\) chords that connect two of these points. Four of these 21 chords are selected at random. What is the probability that these four chosen chords form a bow-tie quadrilateral?

 

Please help! Thanks! smiley

 Aug 10, 2020
 #1
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The answer is 2/399.

 Aug 10, 2020
 #2
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@answer #1: Thanks for your answer, but I want to understand HOW to do this problem and I don't want just the answer. Could you please tell me how you did the problem? Thanks! smiley

Guest Aug 12, 2020

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