KöMaL 2007 B4003

$P_1,P_2,\ldots,P_{2007}$ are given points in the plane, no three of which are collinear. Show that for all 1$\le i \le$2007 there is an even number of triangles $P_j P_k P_l$ that contain $P_i$ in the interior. (British competition problem)