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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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Bunuel
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Of the 12 points in a given plane 5 are on circle O and remaining 7 ar [#permalink] 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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kt9696
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Re: Of the 12 points in a given plane 5 are on circle O and remaining 7 ar [#permalink] New post   03 Jan 2020, 05:10
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[quote="Bunuel"]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


Here's my approach:

Total points in the given plane = 12
Total triangles possible (if none of them were collinear) = 12C3
BUT, 7 points are collinear, so 7C3 triangles cannot be formed.

So, 12C3 - 7C3 = 185 triangles
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nick1816
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Re: Of the 12 points in a given plane 5 are on circle O and remaining 7 ar [#permalink] 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


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Archit3110
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Of the 12 points in a given plane 5 are on circle O and remaining 7 ar [#permalink] New post   Updated on: 26 Nov 2019, 08:56
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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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exc4libur
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Re: Of the 12 points in a given plane 5 are on circle O and remaining 7 ar [#permalink] 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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jfranciscocuencag
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Re: Of the 12 points in a given plane 5 are on circle O and remaining 7 ar [#permalink] New post   21 Dec 2019, 17:50
Can someone plz give an explanation?

Kind regards!
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shiva1325
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Re: Of the 12 points in a given plane 5 are on circle O and remaining 7 ar [#permalink] New post   04 Jan 2020, 23:11
as given
there are 5 points on circle O and 7 points on line L
now case 1: where triangles are formed by the points taking only on circle
This is done in 5c3 ways=10
case 2: where 2 points on circle and one point on Line (as no two points on cirlce and one point on straight line are collinear)
this can be done in 5c2*7c1 ways=70
case 3: where 1 point on circle and 2 points on straight line
this can be done in 5c1*7c2 ways=105
=>10+70+105=185 ways a triangle can be formed
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Fdambro294
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Of the 12 points in a given plane 5 are on circle O and remaining 7 ar [#permalink] New post   25 May 2021, 01:00
3 scenarios (since only the 7 points on the line will be the only time when 3 or more points are collinear)

Scenario 1:
Choose any 2 points from the circle and 1 point from the line:

5! / (2! 3!) * 7 = 70 ways

OR

Scenario 2: choose any 2 points from the line and a 3rd point from the circle

7! / (2! 5!) * 5 = 105

OR

Scenario 3: can create a triangle completely inscribed in the circle by choosing any 3 points from the circle’s circumference

5! / (3! 2!) = 10

70 + 105 + 10 =


185

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Re: Of the 12 points in a given plane 5 are on circle O and remaining 7 ar [#permalink] New post   14 Dec 2022, 15:01
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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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