There are m points on one straight line AB and n points on another straight line AC, none of them being A. How many triangles can be formed with these points as vertices?
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Correct answer: B. ½ mn(m + n − 2)
Explanation
Choose 2 points on AB and 1 on AC (C(m,2)·n) or 1 on AB and 2 on AC (m·C(n,2)). Total = mn(m − 1)/2 + mn(n − 1)/2 = ½ mn(m + n − 2).More Discrete Structures and Optimisation questions
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