There are three coplanar parallel lines. If any `p`points aretaken on each of the lines, the maximum number of triangles with vertices onthese points isa. `3p^2(p-1)+1`b. `3p^2(p-1)`c. `p^2(4p-3)`d. none of theseA. `3n^(2)(n-1)`B. `3n^(2)(n-1)+1`C. `n^(2)(4n-3)`D. none of these

There are three coplanar parallel lines. If any `p`points aretaken on

1.	There are three coplanar parallel lines. If any `p`points aretaken on each of the lines, the maximum number of triangles with vertices onthese points isa. `3p^2(p-1)+1`b. `3p^2(p-1)`c. `p^2(4p-3)`d. none of theseA. `3n^(2)(n-1)`B. `3n^(2)(n-1)+1`C. `n^(2)(4n-3)`D. none of these
Answer» The maximum number of triangles = Number of triangles with vertices on different lines + Number of trigangles with 2 vertices on one line and third vertex on any one of the remaining two lines `=""^(n)C_(1)xx""^(n)C_(1)xx""^(n)C_(1)+""^(3)C_(1)xx(""^(n)C_(2)xx""^(2n)C_(1))=3n^(2)(n-1)`.

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There are three coplanar parallel lines. If any `p`points aretaken on each of the lines, the maximum number of triangles with vertices onthese points isa. `3p^2(p-1)+1`b. `3p^2(p-1)`c. `p^2(4p-3)`d. none of theseA. `3n^(2)(n-1)`B. `3n^(2)(n-1)+1`C. `n^(2)(4n-3)`D. none of these

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