The number of triangles that can be formed by | vedclass

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(C) To form a triangle,we need $3$ non-collinear points.Total number of points = $5 + 3 = 8$.The total number of ways to select $3$ points out of $8$

Vedclass · Accepted Answer

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

Vedclass · Answer

(C) To form a triangle,we need $3$ non-collinear points.Total number of points = $5 + 3 = 8$.The total number of ways to select $3$ points out of $8$ is $^8C_3$.However,if $3$ 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 them is $^5C_3$.There are $3$ points on the other parallel line,so the number of ways to select $3$ collinear points from them is $^3C_3$.Therefore,the number of triangles = Total selections - Collinear selections = $^8C_3 - ^5C_3 - ^3C_3$.

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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