A cellular distributed antenna system with randomly located distributed antenna elements (AEs) and mobile users is considered. The AEs are connected to the base station via an offline dedicated link (such as fiber optics or line-of-sight RF). A user is served by selecting the AE with the best channel to it (often the closest one). The outage probability is derived for both AE selection and user selection individually for an isolated cell, and shown to decrease exponentially with the number of AEs and users. Due to selection diversity, fading and shadowing typically are desirable effects that decrease the likelihood of outage. In a more general setup - with multiple distributed antennas and both AE selection and user selection - the outage probability decreases exponentially with the number of users but not with the number of AEs. Due to diminishing returns, there is no need to deploy more AEs than a certain extent, which is determined by the transmit power of AEs. With a sufficient number of AEs, randomly deployed AEs can provide nearly the same performance as regularly deployed AEs, and both have a common outage probability floor which is determined by user density.