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How many triangles can be formed using 8 points in a given p

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Re: How many triangles can be formed using 8 points in a given p  [#permalink]

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New post 26 Aug 2017, 00:07
1
I think the answer is B and the exact answer for this will have 3 conditions.
Total no of points= 8 points
but 3 collinear points
1. 3 points to make the triangle is from the 5 points which are not collinear
5C3
2. 3 points to make the triangle is from 1 vertex from 3 collinear set and 2 vertex from 5 points set
3C1 * 5C2
3. 2 vertex of the triangle can be from the same collinear line as they can act as base and the 3rd vertex from the other 5 points
3C2 * 5C1

1+2+3= 5C3+3C1*5C2+3C2*5C1
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Re: How many triangles can be formed using 8 points in a given p  [#permalink]

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New post 01 Nov 2017, 02:11
Let's name each of 8 points as a,b,c,d,e,f,g,h

Let's assume that a,b&c are in one straight line, so cannot form a triangle with each other.

Now, total possible Triangle that can be formed choosing any 3 points without any colinear constraint is 8C3 = 56.

Now, out of 56 possible sets of 3 points each, there is one set a-b-c that is incapable of forming a triangle. But, remaining 55 triangle are possible.

Hence, Statement 2 is sufficient and Ans is B.

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Re: How many triangles can be formed using 8 points in a given p  [#permalink]

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New post 27 Feb 2019, 02:45
flyingbunny wrote:
The meaning of "8C3-1" is really brief, clear and precise. That is the beauty of math. I like it and you deserve a kudos for this. :)


Thanks for the concise answer!

I have one question, tho.
Isn't there a condition in making a triangle?
Such as "The added length of 2 sides of a triangle has to be longer than the last side."

How can we rule out this condition?
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Re: How many triangles can be formed using 8 points in a given p  [#permalink]

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New post 03 Jul 2019, 04:36
Bunuel wrote:
Christy111 wrote:
Why can't we just pick all possible combinations of 3 points out of 8 to answer the first question?
8C3 looks sufficient to me
please help


Ask yourself: how many triangles can be formed out of 8 collinear points? Is it 8C3 or 0?


Could you please tell me what equation will be formed for the second statement. Thank you
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Re: How many triangles can be formed using 8 points in a given p   [#permalink] 03 Jul 2019, 04:36

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