# Seven points are marked on the line, and one point is marked outside this line

**Seven points are marked on the line, and one point is marked outside this line. Find the number of all possible triangles with vertices at the eight marked points.**

All triangles will have one of their vertices at a point outside the straight line. Let’s count how many sides of triangles can be obtained by connecting points lying on a straight line. Each of the 7 points can be connected to 6 others. This will turn out 7 6 = 42 segments. But at the same time, we counted each segment twice (point 1 with point 2 and 2 with 1 are the same segment). This means that there will be 21 segments on a straight line, which can be a side of a triangle. By connecting the ends of each line segment to a point outside the straight line, we get 21 triangles.

Answer: 21.