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# There are 15 points in a given plane, no three of which are

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There are 15 points in a given plane, no three of which are [#permalink]  18 Sep 2012, 00:24
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Question Stats:

49% (02:03) correct 51% (01:10) wrong based on 137 sessions
There are 15 points in a given plane, no three of which are on the same line. If one of the points is represented as 'A', then how many triangles can be determined with the 15 points that contain the point A?

A. 91
B. 105
C. 182
D. 210
E. 455
[Reveal] Spoiler: OA

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Last edited by Bunuel on 18 Sep 2012, 00:32, edited 1 time in total.
Renamed the topic and edited the question.
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Re: There are 15 points in a given plane, no three of which are [#permalink]  18 Sep 2012, 00:36
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summer101 wrote:
There are 15 points in a given plane, no three of which are on the same line. If one of the points is represented as 'A', then how many triangles can be determined with the 15 points that contain the point A?

A. 91
B. 105
C. 182
D. 210
E. 455

Any 2 points out 14 points will create triangle with third point A, so the answer is $$C^2_{14}=91$$.

Similar question to practice:
if-4-points-are-indicated-on-a-line-and-5-points-are-132677.html

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WE: General Management (Energy and Utilities)
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Re: There are 15 points in a given plane, no three of which are [#permalink]  18 Sep 2012, 02:40
Fist point is A which is fixed so can be selected in 1 way
Second point can be selected in 14 ways
Third point can be selected in 13 ways
so total ways = 1x14x13 = 182
but answer is 91 which is 182/2
I m confused, where am I wrong
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Re: There are 15 points in a given plane, no three of which are [#permalink]  18 Sep 2012, 03:27
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bhavinshah5685 wrote:
Fist point is A which is fixed so can be selected in 1 way
Second point can be selected in 14 ways
Third point can be selected in 13 ways
so total ways = 1x14x13 = 182
but answer is 91 which is 182/2
I m confused, where am I wrong

Order of choosing the two other points doesn't matter: ABC and ACB is the same triangle.
Therefore, you should divide 182 by 2, because you counted each triangle twice.
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Re: There are 15 points in a given plane, no three of which are [#permalink]  05 Jan 2013, 00:43
summer101 wrote:
There are 15 points in a given plane, no three of which are on the same line. If one of the points is represented as 'A', then how many triangles can be determined with the 15 points that contain the point A?

A. 91
B. 105
C. 182
D. 210
E. 455

$$=\frac{14!}{2!12!} = 91$$
Note: The question specified that no three points lie on the same line. If that is true, the number of triangles would be less. But luckily, no such three points will form a line so rest assured, all will become triangles.
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Re: There are 15 points in a given plane, no three of which are [#permalink]  29 Oct 2014, 09:33
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: There are 15 points in a given plane, no three of which are   [#permalink] 29 Oct 2014, 09:33
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