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5 points are marked on one line and 7 points on a parallel line. How many triangles have their vertices among these 12 points?

Competition practiceProbability & Permutation

A220
B210
C185
D175

Step-by-Step Solution

Two points from one line and one from the other:

^{5} C_{2} \times 7 +^{7} C_{2} \times 5 = 70 + 105 = 175

.

Answer: D) 175

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