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# Club Challenges -- Triangle Problem

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Manager
Joined: 15 Nov 2007
Posts: 135
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Club Challenges -- Triangle Problem [#permalink]  03 Jan 2008, 21:57

If one of two parallel lines has 7 points on it and the other has 8, how many triangles can be drawn using the points?

* 168
* 196
* 316
* 364
* 455

You can take 2 points out of 8 on one line and combine them with one of the 7 points on the other line, or you can take 2 points from the other line and combine them with one of the 8 points on the original line. Algebraically:
7C_8^2+8C_7^2 = 364
Director
Joined: 12 Jul 2007
Posts: 865
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Re: Club Challenges -- Triangle Problem [#permalink]  04 Jan 2008, 06:45
7*8C2 + 8*7C2
7*28 + 8*21
196 + 168 = 364

Imagine these two parallel lines. To form a triangle we need to have 1 point on one of the lines and 2 points on the opposite line.

7*8C2 = 7 ways to choose 1 point multiplied by the number of ways to choose 2 points from the 8 points on the other line

8*7C2 = 8 ways to choose 1 point multiplied by the number of ways to choose 2 points from the 7 points on the other line

add these together and that's your total. This is a combinations problem.
Manager
Joined: 04 Jan 2008
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Re: Club Challenges -- Triangle Problem [#permalink]  05 Jan 2008, 05:04
approach as a combination, you can take 2 points from one line and one from another. then add
7C2 X 8C1 + 8C2 X 7C1
Intern
Joined: 06 Jan 2008
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Re: Club Challenges -- Triangle Problem [#permalink]  06 Jan 2008, 06:45
D) 364

7.8c2 + 8.7c2
Re: Club Challenges -- Triangle Problem   [#permalink] 06 Jan 2008, 06:45
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