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The number of triangles in a complete graph with 10 non-collinear vertices is
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The correct answer is:
120
Consider that there are $m$ collinear points out of total $n$ points in a plane. To construct a triangle we require 3 non-collinear points.
Hence, the number of triangles will be ${ }^{n} C_{3}-{ }^{m} C_{3}$.
Since, all the point in the above question are non-collinear, hence $n=10$ and $m=0$
Therefore, the total number of triangles are $={ }^{10} C_{3}$
$$
=\frac{10 \times 9 \times 8}{3 !}=\frac{90 \times 8}{6}=15 \times 8=120
$$
Hence, the number of triangles will be ${ }^{n} C_{3}-{ }^{m} C_{3}$.
Since, all the point in the above question are non-collinear, hence $n=10$ and $m=0$
Therefore, the total number of triangles are $={ }^{10} C_{3}$
$$
=\frac{10 \times 9 \times 8}{3 !}=\frac{90 \times 8}{6}=15 \times 8=120
$$
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