The number of triangles that can be formed by | vedclass

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(C) Total number of points = $5 + 3 = 8$. To form a triangle,we need to select $3$ points out of $8$,which can be done in $^8C_3$ ways. However,if the

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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 out of $8$,which can be done in $^8C_3$ ways. However,if the $3$ selected points are collinear,they do not form a triangle. There are $5$ points on one line,so the number of ways to select $3$ collinear points from these is $^5C_3$. There are $3$ points on the other parallel line,so the number of ways to select $3$ collinear points from these is $^3C_3$. Thus,the number of triangles = $^8C_3 - ^5C_3 - ^3C_3$.

The number of triangles that can be formed by $5$ points on a line and $3$ points on a parallel line is

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