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GMATD11
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Geometry 02 Feb 2011, 06:59
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How many triangles can be formed in octagon?



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Geometry 02 Feb 2011, 14:12
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GMATD11
How many triangles can be formed in octagon?
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Any 3 points out of 8 in convex octagon will form a triangle, so # of different triangles possible is \(C^3_8=56\).

Similar question: gmat-diagnostic-test-question-79373.html
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intcan
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Geometry 02 Feb 2011, 14:27
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I misunderstood the question. I was thinking of the triangles from one vertex itself. Thanks Bunuel.
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Geometry 16 Feb 2011, 08:32
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Bunuel - 3C8 shouldn't it be 8C3 ?
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Geometry 16 Feb 2011, 08:45
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amma4u
Bunuel - 3C8 shouldn't it be 8C3 ?
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It's just a different way of writing the same: choosing 3 out of 8 (it can not possibly be choosing 8 out of 3, right?).
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Geometry 17 Feb 2011, 10:01
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So if a polygon has n sides, the number of triangles to be formed will be nC3? Thanks!
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Geometry 28 Feb 2011, 19:10
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Bunuel - yes...my bad
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Geometry 05 Mar 2011, 23:40
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how many it can be in pentagon? 5c3?
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Geometry 05 Mar 2011, 23:55
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how many it can be in pentagon? 5c3?
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True, because there are no set of 3 collinear points in a pentagon.

If there are n non-collinear points, where n>=3, we can make \(C^n_3\) triangles out of it.

If there is one set of x collinear points out of n points, where x>=3 and n>=x, then we can make

\(C^n_3-C^x_3\) triangles.



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