How many triangles can be formed using 5 poin | vedclass

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(C) Total number of points = $5 + 3 = 8$. To form a triangle,we need to select $3$ points that are not collinear. The total number of ways to select $

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$^8C_3 - ^5C_3 - ^3C_3$

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(C) Total number of points = $5 + 3 = 8$. To form a triangle,we need to select $3$ points that are not collinear. The total number of ways to select $3$ points from $8$ is $^8C_3$. However,selecting $3$ points from the $5$ collinear points on the first line does not form a triangle. Similarly,selecting $3$ points from the $3$ collinear points on the second line does not form a triangle. Therefore,the number of triangles = $^8C_3 - ^5C_3 - ^3C_3$. Calculating the values: $^8C_3 = \frac{8 	imes 7 	imes 6}{3 	imes 2 	imes 1} = 56$,$^5C_3 = \frac{5 	imes 4}{2 	imes 1} = 10$,and $^3C_3 = 1$. Number of triangles = $56 - 10 - 1 = 45$.

How many triangles can be formed using $5$ points on a line and $3$ points on a parallel line?

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