There are 10 points in three parallel planes, the first plane contain 5 points, the second plane contains 3 points and the third plane contain rest of them, then how many triangles to be formed?
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Answer:
11 triangles can be formed.
Step-by-step explanation:
{ Given that the three planes are parallel to each other, but not coplanar for sure. }
The first plane contains 5 points. Then the number of triangles can be forced from the points is ⁵C₃ = 10.
The second plane contains 3 points and only 1 triangle can be formed from it.
The third plane contains 2 points and thus no triangle can be formed.
Since the planes aren't coplanar, we cannot connect the points from one plane to another.
Therefore the number of required triangles is (10 + 1) = 11
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