Five points in the plane are given, no three of which are collinear. Show that some four of them form a convex quadrilateral.
This question seems very simple but also at the same time very interesting. I have tried drawing many sets of $5$ dots and they all seem to have at least $1$ pair of $4$ form a convex quadrilateral, but how do I show that they all can't be concave? A concave quadrilateral is a quadrilateral in which at least one of its diagonals is not contained or is partly not contained in the quadrilateral.
Also, I am a bit confused on the case where $4$ points don't form a convex hull. We then have a triangle with $2$ points in it. How does this guarantee a convex quadrilateral?