Let be three events, where . Also, . Using the inclusion-exclusion principle,

Thus, I would like to prove that subject to has solution . In order to do this I used Lagrange multipliers, and after a few manipulations on the equations, I come up with this answer.

: how can I generalize this for events? More specifically, I want to prove that subject to has solution .THE QUESTION IS

PS: Some directions to solve this problem would be useful too (or a reference where it was already solved).....