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The straight lines l1, ,l2 & l3, are...

The straight lines `l_1, ,l_2 & l_3`, are parallel & lie in the same plane. A total of m points are taken on the line `l_1`, n points on `l_2, & k` points on `l_3`. How many maximum number of triangles are there whose vertices are at these points ?

Text Solution

Verified by Experts

The correct Answer is:
`""^(m + n + k)C_(3) -( ""^(3)C_(3) + ""^(n)C_(3) + ""^(k)C_(3))`
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Knowledge Check

  • Three straight lines L_1, L_2 and L_3 are parallel and lie in the same plane. A total of m points are taken on L_1 , n points on. L_2 , K points on L_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 - ^mC_3 - ^nC_3`
    C
    `^(m+n+k) C_3 + ^mC_3 + ^nC_3`
    D
    None of these

  • The straight lines l_1 ,l_2 ,l_3 are parallel and lie in the same plane. A total number of m points on l, n points on l_2 ,k points on l_3 are used to produce the triangles, the maximum number of triangles formed with vertices at these points are:

    A
    `""^(m)C_3xx ""^(n)C_3 xx ""^(k)C_3`
    B
    `""^((m+n+k))C_3-(""^(m)C_3 +""^(n)C_3"""^(k)C_3)`
    C
    `""^((m+n+k))C_3`
    D
    none of these

  • The straight lines l_1,l_2,l_3 are parallel and lie in the same plane. A total number of m points on l_1 n points on l_2 k points on l_3 are used to produce the triangles, the maximum number of triangles formed with vertices at these points are :

    A
    `"^mC_3xx^nC_3xx^kC_3`
    B
    `^(m+n+k)C_3 -("^mC_3+^nC_3+^kC_3)`
    C
    `"^(m+n+k)C_3`
    D
    none of the above

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