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How many triangles can be formed by joining 12 points, 7 of which are [#permalink]
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Question Stats: Hide Show timer StatisticsHow many triangles can be formed by joining 12 points, 7 of which are collinear?A. 255B. 220 C. 185D. 35 E. 10 _________________
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How many triangles can be formed by joining 12 points, 7 of which are [#permalink] The number of triangles that can be formed from 12 points is \(5C_3\) = 10 as 7 points are collinear. E is the answer.
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How many triangles can be formed by joining 12 points, 7 of which are [#permalink]
Bunuel wrote: How many triangles can be formed by joining 12 points, 7 of which are collinear?A. 255B. 220 C. 185D. 35 E. 10 given 7 points are collinear ,which means 7 out of 12 points are on same line and 5 are random pointsso total triangles which can be formed ; 7c2*5c1+7c1*5c2+5c3 = 21*5+7*10+10 = 185IMO C
Originally posted by Archit3110 on 29 Jan 2019, 01:49.
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Re: How many triangles can be formed by joining 12 points, 7 of which are [#permalink]
Solution Given:
To find:
Approach and Working:
• Therefore, \(N = ^7C_2 * ^5C_1 + ^7C_1 * ^5C_2 + ^5C_3 = 21 * 5 + 7 * 10 + 10 = 185\) Answer: C
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How many triangles can be formed by joining 12 points, 7 of which are [#permalink]
Bunuel wrote: How many triangles can be formed by joining 12 points, 7 of which are collinear?A. 255B. 220 C. 185D. 35 E. 10 We can start with 12C3 to get \(\frac{12*11*10}{3!} = 2*11*10\) random selections. The problem with that random selection is the 7 collinear points, if we pick 3 points on the same line it will not form a triangle so we need to eliminate 7C3 = \(\frac{7*6*5}{3!} = 7*5\) selections.2*11*10 - 7*5 = 220 - 35 = 185.Ans: C _________________
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Re: How many triangles can be formed by joining 12 points, 7 of which are [#permalink] We can solve by finding total triangles formed by 12 points and then subtract those by the total triangles formed by 7 points ( as they are collinear ). 12C3-7C3= 185. Hence,C Posted from my mobile device
Re: How many triangles can be formed by joining 12 points, 7 of which are [#permalink] 04 Oct 2020, 13:25 |
How many straight lines can be formed by joining 12 points 7 of which are in the same line?
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