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There are three parallel straight lines

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mensanumber Senior | Next Rank: 100 Posts Default Avatar
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There are three parallel straight lines

Post Tue Mar 06, 2018 11:55 pm
There are three parallel straight lines. Two points A and B are marked on the first line, points C and D are marked on the second line and points E and F are marked on the third line. Each of these six points can move to any position on its respective straight line. What is the maximum number of triangles that can be drawn from these points?

1) 41
2) 40
3) 18
4) 44

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Post Wed Mar 07, 2018 11:21 am
mensanumber wrote:
There are three parallel straight lines. Two points A and B are marked on the first line, points C and D are marked on the second line and points E and F are marked on the third line. Each of these six points can move to any position on its respective straight line. What is the maximum number of triangles that can be drawn from these points?

1) 41
2) 40
3) 18
4) 44
From the 6 points, ANY COMBINATION OF 3 can serve to form a triangle.
Thus:
Maximum number of triangles that can be formed from the 6 points = number of ways to choose 3 points from 6 options = 6C3 = (6*5*4)/(3*2*1) = 20.

The correct answer does not seem to be among the answer choices.
What is the source?

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