Permutation Problems and Special Functions
Richard Askey, Mourad E. H. Ismail · Canadian Journal of Mathematics · 1976
Suppose we have n events Ai, … , An and let p(Aj1 … , Ajk) be the probability that the events Ah, . . . , Ajk occur jointly. The probability P0 that none of Ai, . . . , An occur is given by Poincaré's formula, the probabilistic version of the principle of inclusion and exclusion: