Problem

The key is to recognize that a valid triangle needs three vertices from three different sides of the quadrilateral. Start by counting all possible ways to choose one point from each of three sides, then subtract cases where those three points are collinear (which won't form a triangle). Since the points lie on the sides of a convex quadrilateral, collinearity only happens when all three points come from sides that share a common vertex—but we're already choosing from different sides, so no three points are collinear. This means every selection of three points from three different sides automatically forms a triangle.

The key is to recognize that a valid triangle needs three vertices from three different sides of the quadrilateral. Start by counting all possible ways to choose one point from each of three sides, then subtract cases where those three points are collinear (which won't form a triangle). Since the points lie on the sides of a convex quadrilateral, collinearity only happens when all three points come from sides that share a common vertex—but we're already choosing from different sides, so no three points are collinear. This means every selection of three points from three different sides automatically forms a triangle.