Question 4

# Ten points are marked on a straight line and eleven points are marked on another straight line. How many triangles can be constructed with vertices from among the above points?

Solution

For a triangle to be formed, we need three points.

Case 1: Select 2 points on the line that has 10 points and 1 point on the line that ha 11 points.

This can be done in $$^{10}C_2$$*$$^{11}C_1$$ ways = 495 ways.

Case 2: Select 2 points on the line that has 11 points and 1 point on the line that ha 10 points.

This can be done in $$^{11}C_2$$*$$^{10}C_1$$ ways = 550 ways.

495 + 550 = 1045 ways.