SOLUTION: how many polygons can be possibly formed from 5 distinct points on a plane,no three of which are collinera

Question 1178815: how many polygons can be possibly formed from 5 distinct points on a plane,no three of which are collinera

Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

This might be a hard question. We first characterize the polygons according to the number of sides and then calculate the maximum count of them. So we will be sure that there is nothing “regular” about the distribution of the points.
3-sides: There are ways to choose of the points
4-sides: There are ways to choose of the points.
For each choice, there is one concave way to join them and two self-crossing ways.

A convenient way to think about this is to count the number of Hamiltonian Cycles in a 4-graph and that is .
-sides: The number of Hamiltonian cycles on vertices is .
Total:

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