I will present an estimate of Ming-Liang Cai for the number of ends of a Riemannian manifold with nonnegative Ricci curvature outside a compact set. The main tools of the proof will be the Cheeger-Gromoll splitting theorem and Bishop-Gromov's volume comparison theorem. If time permits I will also talk about a subsequent result of Cai et al. on the case when the compact set is small.