Three straight lines $$l1$$,$$l2$$ and $$l3$$ are parallel and lie in the same plane. Five points are taken on each of $$l1$$,$$l2$$ and $$l3$$. The maximum number of triangles which can be obtained with vertices at these points, is

Question

Three straight lines  $$l1$$,$$l2$$  and  $$l3$$ are parallel and lie in the same plane. Five points are taken on each of $$l1$$,$$l2$$ and  $$l3$$. The maximum number of triangles which can be obtained with vertices at these points, is

Infinity Learn · Accepted Answer

The total number of points is $$15$$. From these $$15$$ points we can obtain  $$15C3$$ triangles. However, if all the $$3$$ points are chosen on the same straight line, we do not get a triangle. Therefore, the required number of $$triangles=15C3$$−$$3$$ $$5C3=425$$

Three straight lines $l_{1}, l_{2}$ and $l_{3}$ are parallel and lie in the same plane. Five points are taken on each of $l_{1}, l_{2}$ and $l_{3}$ . The maximum number of triangles which can be obtained with vertices at these points, is

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

Three straight lines l1,l2 and l3 are parallel and lie in the same plane. Five points are taken on each of l1,l2 and l3. The maximum number of triangles which can be obtained with vertices at these points, is

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

Three straight lines $l_{1}, l_{2}$ and $l_{3}$ are parallel and lie in the same plane. Five points are taken on each of $l_{1}, l_{2}$ and $l_{3}$ . The maximum number of triangles which can be obtained with vertices at these points, is