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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 \(\dbinom{7}{2} = 21\) chords that connect two of these points. Four of these  chords are selected at random. What is the probability that these four chosen chords form a bow-tie quadrilateral?

 Jul 18, 2020
 #1
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The probability is 3*C(7,3)/C(21,4) = 1/57.

 Jul 18, 2020
 #2
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"is shown below"  Where it the pic?

 Jul 18, 2020

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