Question 199702
The first part of the question uses combinations. Since running a line through points A and B makes no difference from running a line through points B and A, we know this is a combination problem (not a permutation problem) since order does not matter.

Therefore,  2 Choose 8  is the number of lines determined by 8 points, since a line consists of only 2 points.


The second part of the question uses the same concept, only now, 3 points are involved (consisting of the triangle's vertices.)  3 Choose 8.