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How many triangles with positive area can be drawn on the

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Joined: 14 Aug 2017
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Re: How many triangles with positive area can be drawn on the [#permalink]

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New post 03 Oct 2017, 02:05
Bunuel Thanks for the clarification.
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Re: How many triangles with positive area can be drawn on the [#permalink]

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New post 31 Dec 2017, 01:44
Can anyone please highlight the difference between the question under discussion and this question https://gmatclub.com/forum/triangle-abc ... 32573.html

How do we distinguish between the two?
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How many triangles with positive area can be drawn on the [#permalink]

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New post 31 Dec 2017, 02:36
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Rw27 wrote:
Can anyone please highlight the difference between the question under discussion and this question https://gmatclub.com/forum/triangle-abc ... 32573.html

How do we distinguish between the two?


The main difference is the constraints.

In this question you are free to choose any 3 points on the plane (and then have to remove colinearities).
This means you choose 3 x coordinates and 3 y coordinates.
So the calculation is 9C3 - colinearities.
Colinearities in this problem are when all three points are on the same line and as explained above there are 8 such points.

In the question you linked to the constraints are much stronger:
Essentially, once you choose points A and C then point B is fixed.
So you're only choosing 2 x coordinates and 2 y coordinates.
You can do this as explained in the link - 6C1 * 11C1 * 5C1 * 10C1 = 3300
You can also calculate 66*(65-colinearities) = 66*50 = 3300
Colinearities in this problem are when points A and C are on the same line and there are 15 such options (10 horizontal, 5 vertical)

If all this is confusing, the bottom line is that the constraints are the main difference - are you choosing 3 points or 2?
Good luck!
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How many triangles with positive area can be drawn on the   [#permalink] 31 Dec 2017, 02:36

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