Exercise 4. We are given 20 points in the plane such that no three of them are collinear. How many lines can be formed passing through two of these points?
Solution to exercise 4 We choose a point $A$: there are 20 possibilities. Then we choose a point $B$ different from $A$: there are 19 possibilities. We then draw the line connecting $A$ to $B$. Each line has been drawn exactly twice, so there are $19 \times 20 / 2=190$ lines.