The straight lines `I_(1),I_(2),I_(3)` are parallel 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

Options

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

Answer

B

Explanation

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)`