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A plane has six points and no three of the points are collinear. How m

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Russ19
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A plane has six points and no three of the points are collinear. How m [#permalink] New post   26 Jan 2020, 10:17
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A plane has six points and no three of the points are collinear. How many distinct triangles can be drawn that have three of the points in the plane as vertices?

A) 15

(B) 18

(C) 20

(D) 30

(E) 216

Source: GMAT Quantum Math Course
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rajatchopra1994
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Re: A plane has six points and no three of the points are collinear. How m [#permalink] New post   26 Jan 2020, 22:51
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sjuniv32 wrote:
A plane has six points and no three of the points are collinear. How many distinct triangles can be drawn that have three of the points in the plane as vertices?

A) 15

(B) 18

(C) 20

(D) 30

(E) 216

Source: GMAT Quantum Math Course


Explanation:
Selecting 3 points from 6 to form a triangle: 6C3
= 6!/3!*3!
= 6*5*4*3!/3!*3!
= 120/6
= 20 ways

IMO-C
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ajaymahadev
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Re: A plane has six points and no three of the points are collinear. How m [#permalink] New post   26 Jan 2020, 22:58
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to make a triangle, we need 3 points. It is given that no 3 points are collinear, which makes things easier for us.

all we have to do is select 3 points out of the 6 points and this can be done in 6C3 ways or 20 ways.
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Re: A plane has six points and no three of the points are collinear. How m [#permalink] New post   23 Feb 2020, 08:05
I still did not understand this P.S and it's solution. Can anyone help me with explanation.

thanks for your help in advance.
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shiva1325
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Re: A plane has six points and no three of the points are collinear. How m [#permalink] New post   23 Feb 2020, 09:53
nislam wrote:
I still did not understand this P.S and it's solution. Can anyone help me with explanation.

thanks for your help in advance.


given that there are six points and no three points are collinear which means the six points are randomly placed such that no three points lie on a straight line
and now since the points are placed randomly we can select any three points form the six points and form a triangle
we can select 3 points from six points in 6c3 ways =20

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Re: A plane has six points and no three of the points are collinear. How m [#permalink]
23 Feb 2020, 09:53
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