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

Let $l_1$ and $l_2$ be two lines intersecting at $P$. If $A_1, B_1, C_1$ are points on $l_1$,and $A_2, B_2, C_2, D_2, E_2$ are points on $l_2$,and if none of these points coincides with $P$,then the number of triangles formed by these eight points is:

How many different (mutually non-congruent) trapeziums can be constructed using four distinct side lengths from the set $\{1, 2, 3, 4, 5, 6\}$?

Let $p_n$ denote the total number of triangles formed by joining the vertices of an $n$-sided regular polygon. If $p_{n+1} - p_n = 66$, then the sum of all distinct prime divisors of $n$ is:

The number of diagonals in a convex polygon with $n$ sides is .....

$110$ triangles can be formed by joining $10$ points as vertices,in which $n$ points are collinear. Then the value of $n$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module