Number of Sets of Points Containing a Given Point in its Convex Hull

Question

Consider a lattice grid $[0,N]\times [0,N]$ and a given point $P$ inside the grid. Denote the set of lattice points as $S$ (of course, $|S|=(N+1)^2$). I'd like to ask how to count the number of subsets of $S$ containing $P$ inside its convex hull (we allow $P$ lying on the convex hull and the points in the subset can be collinear.). How about containing $P$ strictly inside the convex hull?