Question 28
Let $S$ be a set of $a+b+3$ points on a sphere, where $a, b$ are nonnegative integers and no four points of $S$ are coplanar (that is, no four points lie on a plane). Determine how many planes pass through three points of $S$ and separate the remaining points into $a$ points on one side of the plane and $b$ points on the other side.