In this paper, we consider the amplify-and-forward relaying systems with the relay selection (AF-RS) using full channel information (FCI) and using partial channel information (PCI), respectively, in which the direct communication link between a source and a destination is available. And, the outage probabilities for the AF-RS using FCI and using PCI are investigated in Rayleigh fading channels, respectively. We provide exact outage probabilities, tight outage probability lower bounds, and asymptotic outage probabilities, respectively. And also, we present coding gains achievable by the AF-RS using FCI and using PCI. Through numerical investigation, all the analytic expressions are verified, and the coding gains are respectively evaluated with different average channel powers for the first and the second hop as well as different numbers of relays.