Ten points are marked on a straight line and 11 points are marked on another parallel straight line. How many triangles can be constructed with vertices among the above points?
Solution
For a triangle, we need 3 non collinear points. It means that all 3 points can not lie on a single line.
Case 1: 2 points on Line 1 and 1 point on Line 2 = 10C2 * 11C1 = 495.
Case 2: 1 point of Line 1 and 2 points on Line 2 = 10C1 * 11C2 = 550.
Total number of triangles that can be formed are 1045.
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