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S is a set of points in the plane. How many distinct triangles can be

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Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
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Re: S is a set of points in the plane. How many distinct triangles can be  [#permalink]

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23 Jul 2018, 21:23
ENEM wrote:
what does 'no three of the points in S are collinear' mean?
Also is this really a sub 600 level question? Shouldn't it be at least 600-700 level?

"Collinear" means lying on the same straight line.

3 points are collinear when you can draw a line that passes through all 3 of them. If this happens, the three points cannot make a triangle.
Note that you can always draw a line with any two points by just joining the 2 points.
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[b]Karishma
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Re: S is a set of points in the plane. How many distinct triangles can be  [#permalink]

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23 Jul 2018, 21:33
KarishmaB

Hi,

no I meant what does it mean 'no three points' every three points in set S? What does that mean?
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Re: S is a set of points in the plane. How many distinct triangles can be  [#permalink]

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24 Jul 2018, 00:38
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ENEM wrote:
KarishmaB

Hi,

no I meant what does it mean 'no three points' every three points in set S? What does that mean?

It means no matter which 3 points you pick up, they will not be collinear.
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[b]Karishma
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Re: S is a set of points in the plane. How many distinct triangles can be  [#permalink]

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25 Jul 2018, 03:42
walker wrote:
C

1. we cannot create triangles for 5 points of a line but can do that for points that are not collinear. insuff.
2. we don't know the number of points insuff.

1&2 $$C^5_3=\frac{5*4*3*2}{3*2*2}=10$$

Can you please write formula to calculate the number of triangles if only 3 points are coliner
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Re: S is a set of points in the plane. How many distinct triangles can be  [#permalink]

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25 Jul 2018, 09:49
1
kablayi wrote:
walker wrote:
C

1. we cannot create triangles for 5 points of a line but can do that for points that are not collinear. insuff.
2. we don't know the number of points insuff.

1&2 $$C^5_3=\frac{5*4*3*2}{3*2*2}=10$$

Can you please write formula to calculate the number of triangles if only 3 points are coliner

Hello

Ok, here's a general formula for calculating possible number of triangles.

If there are N points in a plane, and no three of them are collinear, then the number of possible triangles = N(C)3. (number of possible selections of 3 objects from N objects)

If there are N points in a plane, and X of them are collinear, then the number of possible triangles = N(C)3 - X(C)3. (subtracting number of possible selections of 3 objects from X FROM number of possible seelctions of 3 objects from N).

Now to answer your question: IF we were given that there are 5 points in a plane, out of which 3 are collinear, then number of possible triangles would have been = 5C3 - 3C3 = 10 - 1 = 9. Thus 9 triangles would have been possible.
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Re: S is a set of points in the plane. How many distinct triangles can be  [#permalink]

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12 Aug 2018, 03:20
KarishmaB wrote:
ENEM wrote:
KarishmaB

Hi,

no I meant what does it mean 'no three points' every three points in set S? What does that mean?

It means no matter which 3 points you pick up, they will not be collinear.

Dear Karishma / all,

I'm struggling to understand one thing: as a plane is not always a polygon, can the attached image be considered as a 5-point plane which satisfies the 2 conditions per the question ? If so, then wouldn't the answer suppose to be E as we cant confirm the number of triangles then ?

Attachments

5 points plane.png [ 31.57 KiB | Viewed 277 times ]

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Re: S is a set of points in the plane. How many distinct triangles can be  [#permalink]

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11 Sep 2018, 17:42
Bunuel wrote:
GGUY wrote:
S is a set of points in the plane. How many distinct triangles can be drawn that have three of the points in S as vertices?

(1) The number of distinct points in S is 5.
(2) No three of the points in S are collinear.

l got A. What does collinear mean?

Collinear points are those that lie on the same straight line. BTW the correct answer is C, not A. Check the solutions above and ask if anything remains unclear.

To be fair, I didn't even understand the question nor the answers given.
Re: S is a set of points in the plane. How many distinct triangles can be &nbs [#permalink] 11 Sep 2018, 17:42

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