Three straight lines $L_{1}, L_{2}, L_{3}$ 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

^{m + n + k} C_{3}

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^{m + n + k} C_{3} -^{m} C_{3} -^{n} C_{3}

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^{m + n + k} C_{3} +^{m} C_{3} +^{n} C_{3}

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None of the above

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Solution

The correct option is C None of the above
For a triangle, we need $3$ non-collinear points.
There are a total of $m + n + k$ points of which $m, n, k$ are separately collinear.
Hence, number of triangles $=^{m + n + k} C_{3} -^{m} C_{3} -^{n} C_{3} -^{k} C_{3}$
Hence, (d) is correct.

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The straight lines $L_{1}, L_{2}, L_{3}$ are parallel and lie in the same plane. A total number 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

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(b) ^{m + n + k}C₃ – ^mC₃ – ⁿC₃ – ^kC₃
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The straight lines $I_{1}, I_{2}, I_{3}$ are parallel and lie in the same plane. A total number of m points 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

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Q. The straight lines L1, L2, L3 are parallel and lie in the same plane. A total number of

m

points are taken on L1.

n

points on L2 and

k

points on L3. Then maximum number of triangles formed with vertices at these points are:

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Three straight lines L1,L2,L3 are parallel and lie in the same plane. A total of m points are taken on L1, n points on L2, k points on L3, the maximum number of triangles formed with vertices at these points are

The correct option is C None of the aboveFor a triangle, we need 3 non-collinear points.There are a total of m+n+k points of which m,n,k are separately collinear.Hence, number of triangles =m+n+kC3−mC3−nC3−kC3Hence, (d) is correct.

Three straight lines $L_{1}, L_{2}, L_{3}$ 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

The correct option is C None of the above
For a triangle, we need $3$ non-collinear points.
There are a total of $m + n + k$ points of which $m, n, k$ are separately collinear.
Hence, number of triangles $=^{m + n + k} C_{3} -^{m} C_{3} -^{n} C_{3} -^{k} C_{3}$
Hence, (d) is correct.