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?

FocusedPi Apr 16, 2021

#2**+1 **

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.

Melody Apr 16, 2021