l_1, l_2, l_3 are three parallel lines in the | vedclass

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(B) The total number of points is $m + n + k$. Total ways to select $3$ points from these is $^{m+n+k}C_3$. However,points lying on the same line cann

Vedclass · Accepted Answer

$^{m+n+k}C_3 - ^mC_3 - ^nC_3 - ^kC_3$

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(B) The total number of points is $m + n + k$. Total ways to select $3$ points from these is $^{m+n+k}C_3$. However,points lying on the same line cannot form a triangle. Number of triangles formed by $3$ points on line $l_1$ is $^mC_3$. Number of triangles formed by $3$ points on line $l_2$ is $^nC_3$. Number of triangles formed by $3$ points on line $l_3$ is $^kC_3$. Therefore,the number of triangles that can be formed is $^{m+n+k}C_3 - ^mC_3 - ^nC_3 - ^kC_3$.

$l_1, l_2, l_3$ are three parallel lines in the same plane. If there are $m$ points on $l_1$,$n$ points on $l_2$,and $k$ points on $l_3$,what is the maximum number of triangles that can be formed with vertices at these points?

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