The straight lines l1, l2 and l3 are parallel and lie in the same plane. A total number of m points are taken on l1, n points on l2, k 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 + kC3 numbers 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 mC3 or nC3 or kC3 triangle can not be formed
∴ The required number of triangles is m + n + kC3 − mC3 − nC3 − kC3
Hence, the correct answer is option B.
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