Connected Square

Question

Fix a positive integer $n$ and a positive real number $a$. $n$ points are selected uniformly at random from the square with vertices $(\pm a, \pm a)$ in the plane. Afterwards, each pair of points is connected by a line segment. Find the expected number of total intersections between the line segments and the coordinate axes ($x-$axis and $y-$axis). Note that we are not counting intersections between line segments themselves. Report the answer when $n = 10$ and $a = 4$.