2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/158112We compute the growth series and the growth functions of reducible and pseudo-Anosov elements of the pure mapping class group of the sphere with four holes with respect to a certain generating set. We prove that the ratio of the number of pseudo-Anosov elements to that of all elements in a ball with center at the identity tends to one as the radius of the ball tends to infinity.8 pages, 1 figureGeometric Topology57N05; 20F38text