three points that are not on a line determine three lines. how many lines are determined by 9 points, no three of which are on a line?
why is the answer: 9(C)2 = 36 lines
... because a line is defined by two points : the number of lines equals the number of pairs of points you can make. There is no consideration of order because the line is the same as and we are sure that two different pairs define two different lines because there is not three point which are on a line. As is precisely the number of such pairs, it is also the number of lines you're looking for.