Q. Three straight lines $L_{1},\ L_{2},\ L_{3}$ are parallel and lie in the same plane. A total of $m$ points are taken on $L_{1},\ n$ points on $L_{2},\ k$ points on $L_{3}$. The maximum number of triangles formed with vertices at these points are
A) $\ ^{m + n + k}C_{3}$
B) $\ ^{m + n + k}C_{3} - \ ^{m}C_{3} - \ ^{n}C_{3}$
C) $\ ^{m + n + k}C_{3} + \ ^{m}C_{3} + \ ^{n}C_{3}$
D) None of the above
Explanation
(d)
Total number of points on a three lines are $m + n + k$
$\therefore$ maximum number of triangles
$= \ ^{m + n + k}C_{3} - \ ^{m}C_{3} - \ ^{n}C_{3} - \ ^{k}C_{3}$
(subtract those triangles in which point on the same line)
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.