Find the number of triangles that can be formed using 14 points in a plane such that 4 points are collinear?
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Given :
14 points in a plane
4 points are collinear.
To find :
Numbers of triangles made by these points
Solution :
There are total 14 points
to make a triangle we have to choose three points from all 14,
but
it is given that 4 points are collinear
So in these four points,we cant choose any three points at once.
To choose r points out of n without any condition, the formula of combination is used as
(equation 1)
If we have n points in a plane in which m points are collinear then number of triangles formed by those n points are :
(equation 2)
By using equation 1 in equation 2.
The number of triangle formed :
So,
number of triangles formed :
So the number of triangles formed = 364 -4 = 360
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