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The straight lines I(1),I(2),I(3) are pa...

The straight lines `I_(1),I_(2),I_(3)` are paralled and lie in the same plane. A total number of m point are taken on `I_(1),n` points on `I_(2)`, k points on `I_(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)-.^(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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