(C) The total number of ways to select $3$ points out of $10$ is given by $^{10}C_3$. $^{10}C_3 = \frac{10 \times 9 \times 8}{3 \times 2 \times 1} = 1

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(C) The total number of ways to select $3$ points out of $10$ is given by $^{10}C_3$. $^{10}C_3 = \frac{10 \times 9 \times 8}{3 \times 2 \times 1} = 120$. Since $6$ points are collinear,they do not form a triangle. The number of ways to select $3$ points from these $6$ collinear points is $^{6}C_3$. $^{6}C_3 = \frac{6 \times 5 \times 4}{3 \times 2 \times 1} = 20$. Therefore,the total number of triangles $N = 120 - 20 = 100$.

Class 11 Mathematics Permutation and Combination Geometrical problems

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There are $10$ points in a plane,out of which $6$ are collinear. If $N$ is the total number of triangles formed by joining these points,then $N=$

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