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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.
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