There are N points on the plane and the probability that the probability that two points are connected is p. What is the expected number of Quadrilaterals you can find? Assume that there is no three points on the same line. A quadrilateral is defined as a set of four edges that bound a polygonal region.
Is there any close form solution to this question? For $N=4$, it is just $p^4$, but $N=5$ we have to consider all the possibilities from 1~5 Quadrilaterals.