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
Hi
... 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 $\displaystyle (AB)$ is the same as $\displaystyle (BA)$ and we are sure that two different pairs define two different lines because there is not three point which are on a line. As $\displaystyle C^2_9$ is precisely the number of such pairs, it is also the number of lines you're looking for.