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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?

 Apr 16, 2021
 #1
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Any help would be greatly appreciated :)

 Apr 16, 2021
 #2
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This has been asked and answered many times before.

 

there are 21 possible chords and you want 4 of them so that is   21C4 = 4985 possible combinations.

 

To make a bow tie you need just 4 points out of 7   which is  7C4 = 35 combinations

 

But how many possible bow ties can you get out of a specific 4 points?  You work it out.

 

And then you finish it.

 Apr 16, 2021

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