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# How many triangles can be formed by joining 12 points, 7 of which are

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Math Expert
Joined: 02 Sep 2009
Posts: 58427
How many triangles can be formed by joining 12 points, 7 of which are  [#permalink]

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29 Jan 2019, 00:44
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Difficulty:

35% (medium)

Question Stats:

65% (01:51) correct 35% (02:19) wrong based on 31 sessions

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How many triangles can be formed by joining 12 points, 7 of which are collinear?

A. 255
B. 220
C. 185
D. 35
E. 10

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How many triangles can be formed by joining 12 points, 7 of which are  [#permalink]

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29 Jan 2019, 01:45
The number of triangles that can be formed from 12 points is $$5C_3$$ = 10 as 7 points are collinear.

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How many triangles can be formed by joining 12 points, 7 of which are  [#permalink]

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Updated on: 29 Jan 2019, 03:57
Bunuel wrote:
How many triangles can be formed by joining 12 points, 7 of which are collinear?

A. 255
B. 220
C. 185
D. 35
E. 10

given 7 points are collinear ,which means 7 out of 12 points are on same line and 5 are random points

so total triangles which can be formed ; 7c2*5c1+7c1*5c2+5c3 = 21*5+7*10+10 = 185
IMO C

Originally posted by Archit3110 on 29 Jan 2019, 02:49.
Last edited by Archit3110 on 29 Jan 2019, 03:57, edited 1 time in total.
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Re: How many triangles can be formed by joining 12 points, 7 of which are  [#permalink]

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29 Jan 2019, 03:50
1

Solution

Given:
• Total number of points = 12
o Number of collinear points = 7

To find:
• The number of triangles that can be formed

Approach and Working:
• The number of triangles that can be formed, N = number of ways of selecting 2 points from 7 and the other from the remaining 5 + the number of ways of selecting 1 from 7 and 2 from the remaining 5 + the number of ways of selecting 3 points from the remaining 5
• Therefore, $$N = ^7C_2 * ^5C_1 + ^7C_1 * ^5C_2 + ^5C_3 = 21 * 5 + 7 * 10 + 10 = 185$$

Hence, the correct answer is Option C

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Re: How many triangles can be formed by joining 12 points, 7 of which are   [#permalink] 29 Jan 2019, 03:50
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