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There are 10 points in a plane, out of these 6 are collinear. If $N$ is the total number of triangles formed by joining these points, then $N=$
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The correct answer is:
$100$
If all 10 points are collinear, then number of triangles formed
${ }^{10} C_3=\frac{10 !}{3 ! 7 !}=\frac{10 \times 9 \times 8}{3 \times 2}=120$
Triangles formed using 6 collinear points ${ }^6 C_3=20$
Therefore, required number of triangles
$120-20=100$
${ }^{10} C_3=\frac{10 !}{3 ! 7 !}=\frac{10 \times 9 \times 8}{3 \times 2}=120$
Triangles formed using 6 collinear points ${ }^6 C_3=20$
Therefore, required number of triangles
$120-20=100$
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