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Of the 12 points in a given plane 5 are on circle O-Geometry-PS

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Of the 12 points in a given plane 5 are on circle O-Geometry-PS  [#permalink]

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New post 25 Aug 2018, 21:39
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Difficulty:

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Question Stats:

44% (01:49) correct 56% (01:36) wrong based on 21 sessions

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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

A) 175

B) 462

C) 70

D) 276

E) 185

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Of the 12 points in a given plane 5 are on circle O-Geometry-PS  [#permalink]

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New post 25 Aug 2018, 22:01
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Harshgmat 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) 175

B) 462

C) 70

D) 276

E) 185


No. of triangles that can be formed by 12 points=12C3 = 220
7 points are on the line that cannot form a triangle but have been included in 12C3, so subtracting those = 12C3-7C3
=220-35 = 185
Answer E.

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Of the 12 points in a given plane 5 are on circle O-Geometry-PS  [#permalink]

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New post Updated on: 25 Aug 2018, 22:20
Harshgmat 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) 175

B) 462

C) 70

D) 276

E) 185


We can form a triangle by choosing any of the 3 points except when all the 3 points are collinear !
=12C3-7C3

12C3- No of ways in which we can choose any 3 points out of 12
7C3- No of ways in which we choose 3 points(all of which are collinear) out of 7 collinear points

Hence answer is 185. E
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Originally posted by GmatDaddy on 25 Aug 2018, 22:06.
Last edited by GmatDaddy on 25 Aug 2018, 22:20, edited 1 time in total.
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Re: Of the 12 points in a given plane 5 are on circle O-Geometry-PS  [#permalink]

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New post 25 Aug 2018, 22:15
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GmatDaddy wrote:
Harshgmat 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) 175

B) 462

C) 70

D) 276

E) 185


We can form a triangle by choosing any of the 3 points except when all the 3 points are collinear !
=10C3-7C3

10C3- No of ways in which we can choose any 3 points out of 10
7C3- No of ways in which we choose 3 points(all of which are collinear) out of 7 collinear points

Hence answer is 185. E


Hi GmatDaddy,
It must be 12C3 instead of 10C3.
I am sure it's a typo.
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Re: Of the 12 points in a given plane 5 are on circle O-Geometry-PS  [#permalink]

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New post 25 Aug 2018, 22:21
yep, it was.
Coorected. Thank you ! :-)
PKN wrote:
GmatDaddy wrote:
Harshgmat 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) 175

B) 462

C) 70

D) 276

E) 185


We can form a triangle by choosing any of the 3 points except when all the 3 points are collinear !
=10C3-7C3

10C3- No of ways in which we can choose any 3 points out of 10
7C3- No of ways in which we choose 3 points(all of which are collinear) out of 7 collinear points

Hence answer is 185. E


Hi GmatDaddy,
It must be 12C3 instead of 10C3.
I am sure it's a typo.

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Re: Of the 12 points in a given plane 5 are on circle O-Geometry-PS   [#permalink] 25 Aug 2018, 22:21
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