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Correct
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21 triangles. 6 with one component. 3 with two components. 5 with three. 4 with four. 2 with five. 1 with seven.
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I'm not sure what you did, but it's not correct.
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Do we consider the boundaries to cause then we have some extra points then doing combination, nC3 - summation mC3, n is number of points, m is colinear points!
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Do not count the boundaries. Assume lines go on to infinity.
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A little bit warmer?
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