So I decided to give a shot on the #453 project euler problem but there is something that confuses me with the numbers given. I decided to start by calculating the possible arrangements of 4 vertices in the 9 vertex grid. To do that I used the binomial coefficient which gives (for the first example) 126 different arrangements. I then removed all non valid arrangements (polygons with straight lines) but the result is smaller than what described. I am probably doing something wrong and I can't figure out what is the issue. Any help is much appreciated!
Edit: Here is the link