There are 12 points in a plane,no three of wh | vedclass

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(D) The total number of ways to select $3$ points out of $12$ is given by $^{12}C_3$. Since $5$ points are collinear,they do not form a triangle when

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$210$

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(D) The total number of ways to select $3$ points out of $12$ is given by $^{12}C_3$. Since $5$ points are collinear,they do not form a triangle when selected together. The number of ways to select $3$ points from these $5$ collinear points is $^{5}C_3$. Therefore,the total number of triangles formed is $^{12}C_3 - ^{5}C_3$. $^{12}C_3 = \frac{12 	imes 11 	imes 10}{3 	imes 2 	imes 1} = 220$. $^{5}C_3 = \frac{5 	imes 4 	imes 3}{3 	imes 2 	imes 1} = 10$. Total triangles = $220 - 10 = 210$.

There are $12$ points in a plane,no three of which are in the same straight line,except $5$ points which are collinear. Then the total number of triangles that can be formed with the vertices at any three of these $12$ points is

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