Let $p_1,\dots, p_5$ be five points, no three of which are collinear.

Question

1) Let $p_1, \dots, p_5$ be five points, no three of which are collinear. How many lines contain two of these five points?

2) If no four of the five points are coplanar, how many planes contain three of the five points?

Answer 1

Every pair determines a line uniquely, hence there are $5\choose 2$ such lines. Similarly, there are $5\choose 3$ such planes