Here's a more in depth solution to how we get the numerator/denominator at the end.
We want to divide the total number of valid quadrilaterals by the total number of chords groups we can choose.
The denominator is the total number of groups of chords we can choose:
- this is simply 28 Choose 4 ( Comes from 28 chords to choose from and selecting 4 for each grouping)
The numerator is the total number of valid quadrilaterals available:
- we already acknowledge that 4 points only have 1 valid quadrilateral ( proof by examining any other config of lines results in crossed lines, i.e not a quadrilateral)
- if 4 points correspond to 1 quadrilateral then we only need to find the different way to choose 4 points from the 8
- this is simply 8 Choose 4 ( Comes from 8 points to choose from and selecting 4 for each single quadrilateral)
Hope this clears things up in case the explanation wasn't through enough!
@QuantQuestionsio