We define a *bow-tie quadrilateral* as a quadrilateral where two sides cross each other. 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?

For some reason I am not able to upload an example of a bow-tie quadrilateral. Sorry!

mathmathj28 Mar 15, 2020

#1

#2**+2 **

First, find the total number of ways four cords can be chosen out of 21 cords.

Can you do that?

Then count the number of bow tie cords there are.

We do this by listing the TYPES of bow tie cords.

Then counting for each cord type, after this, we add them up altogether.

We take the result and divide it by the total number of ways four cords can be chosen out of 21 cords.

TheGreatestOofman
Mar 15, 2020