The straight lines


The straight lines l1l2 and l3 are parallel and lie in the same plane. A total number of m points are taken on l1n points on l2k points on l3. The maximum number of triangles formed with vertices at these points are

(a) m + n + kC3

(b) m + n + kC3 – mC3 – nC3 – kC3

(c) mC3 + nC3 + kC3

(d) mC3 × nC3 × kC3


Here the total number of points are m + n + k .

Which must give m + n + kCnumbers of triangles. 

Since m points lie l1, taking 3 points at a time is mC3.

similarly, from n points on l2, taking 3 points at a time is nC3 and kC3 from k

from these, three points mCor nCor kCtriangle can not be formed 

∴ The required number of triangles is m + kC− mC3  −  nC3  − kC3

Hence, the correct answer is option B. 

Leave a comment