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Of the 12 points in a given plane 5 are on circle O and remaining 7 ar

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Of the 12 points in a given plane 5 are on circle O and remaining 7 ar  [#permalink]

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New post 25 Nov 2019, 01:49
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Of the 12 points in a given plane 5 are on circle O and remaining 7 are on line L. Number of different triangles that can be formed by these 12 points are
(Assume: 2 points on a circle and 1 point on the line are not collinear)

A. 70
B. 175
C. 185
D. 276
E. 462


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Re: Of the 12 points in a given plane 5 are on circle O and remaining 7 ar  [#permalink]

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New post 25 Nov 2019, 04:12
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Bunuel Shouldn't this mention in the question ( 2 points on a circle and 1 point on the line are not collinear)

Total number of triangles
= 5C3+7C1*5C2+7C2*5C1
=10+70+105=185




Bunuel wrote:
Of the 12 points in a given plane 5 are on circle O and remaining 7 are on line L. Number of different triangles that can be formed by these 12 points are

A. 70
B. 175
C. 185
D. 276
E. 462


Are You Up For the Challenge: 700 Level Questions
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Of the 12 points in a given plane 5 are on circle O and remaining 7 ar  [#permalink]

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New post Updated on: 26 Nov 2019, 08:56
we are considering what is the max. no of ∆ that can be formed using all the points
5c3+ 5c1*7c2 + 7c1*5c2 = 105+ 70 ; 185
IMO C




Bunuel wrote:
Of the 12 points in a given plane 5 are on circle O and remaining 7 are on line L. Number of different triangles that can be formed by these 12 points are

A. 70
B. 175
C. 185
D. 276
E. 462


Are You Up For the Challenge: 700 Level Questions

Originally posted by Archit3110 on 25 Nov 2019, 04:20.
Last edited by Archit3110 on 26 Nov 2019, 08:56, edited 1 time in total.
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Re: Of the 12 points in a given plane 5 are on circle O and remaining 7 ar  [#permalink]

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New post 26 Nov 2019, 08:47
Bunuel wrote:
Of the 12 points in a given plane 5 are on circle O and remaining 7 are on line L. Number of different triangles that can be formed by these 12 points are
(Assume: 2 points on a circle and 1 point on the line are not collinear)

A. 70
B. 175
C. 185
D. 276
E. 462


cases circle + line:
5C2*7C1=70
5C1*7C2=105

cases circle:
5C3=10

total=175+10=185

Ans (C)
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Re: Of the 12 points in a given plane 5 are on circle O and remaining 7 ar   [#permalink] 26 Nov 2019, 08:47
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Of the 12 points in a given plane 5 are on circle O and remaining 7 ar

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