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Number of triangles

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Number of triangles

by vishal.pathak » Mon Nov 21, 2011 3:19 am
How many triangles can be formed using 8 points on a given plane when 3 out of these 8 points are colinear

[spoiler]I calculated as 5C3 + 3C2 * 5 + 5C2 * 3. My answer is incorrect. Please help[/spoiler]
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by Ian Stewart » Mon Nov 21, 2011 3:33 am
vishal.pathak wrote:How many triangles can be formed using 8 points on a given plane when 3 out of these 8 points are colinear

I calculated as 5C3 + 3C2 * 5 + 5C2 * 3. My answer is incorrect. Please help
If no three of the points are collinear, the answer would be 8C3 = 56. Since we don't want to count the 1 trio of points which lie in a straight line, the answer must be 8C3 - 1, which is equal to 55.

Your approach is a perfectly good alternative method, and also gives the answer of 55. Is there a chance you made an error in simplifying?
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