520. Given 5 points, any 4 of which do not lie in the same plane. a) How many tetrahedrons exist, the vertices of which are 4 of these points? b) How many planes pass through triples of these points? c) How many lines are determined by pairs of these points?
520. a) $C_{5}^{4}=C_{5}^{1}=5$; b) the number of planes passing through 3 of these 5 points is $C_{5}^{3}=C_{5}^{2}=10$; c) the number of lines passing through 2 of these points is $C_{5}^{2}=C_{5}^{3}=10$, because if no 4 points lie in the same plane, then no 3 lie on the same line.