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The straight lines , l1,l2 and l3 are pa...

The straight lines , `l_1,l_2 and l_3` are parallel and lie in the same plane . A total number of m points are taken on l : n points on `l_2` k points on `l_3` The maximum number of triangle formed with vertices at these points is :

A

`.^(m+n+k)C_(3)`

B

`.^(m+n+k)C_(3)_.^(m)C_(3)-.^(n)C_(3)-.^(k)C_(3)`

C

`.^(m)C_(3)+.^(n)C_(3)+.^(k)C_(3)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
Total points on all three lines`=m+n+k`
`therefore`Maximum number of triangles`=.^(m+n+k)C_(3)-.^(m)C_(3)-.^(n)C_(3)-.^(k)C_(3)`
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