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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

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

Vedclass · Answer

(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?

Similar Questions

In a row,$6$ boys and $6$ girls are arranged at random. Find the probability that all $6$ girls are together.

There are $n$ distinct points on the circumference of a circle. If the number of pentagons that can be formed using these points as vertices is equal to the number of triangles that can be formed,then what is the value of $n$?

$6$ points in a plane are joined in all possible ways by indefinite straight lines. If no two lines are coincident or parallel,and no three lines pass through the same point (with the exception of the original $6$ points),the number of distinct points of intersection is equal to:

How many triangles can be drawn by means of $9$ non-collinear points?

$A$ polygon has $54$ diagonals. The number of sides of this polygon is

Vedclass Test Series

Exam Paper Generator

Online Exam Module