There are 10 points in a plane, out of these 6 are collinear. The number of triangles formed by joining these points, is

# There are 10 points in a plane, out of these 6 are collinear. The number of triangles formed by joining these points, is

1. A

100

2. B

150

3. C

120

4. D

130

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### Solution:

A triangle is obtained by joining three noncollinear points. So number of triangles on joining 3 points out of 10 points =.

But, 6 points are collinear and on joining any three out of these 6, we do not obtain a triangle .

Hence, the required number of triangles

${=}^{10}{C}_{3}{-}^{6}{C}_{3}=120-20=100$.

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