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This letter presents a detailed investigation on the performance of reconfigurable intelligent surface (RIS)-assisted communication system with user scheduling. Depending on the availability of channel state information (CSI) at the RIS, two separate scenarios are considered, namely without CSI and with CSI. Closed-form expressions are derived for the ergodic capacity of the system in both scenarios. It is found that CSI has a significant impact on the performance of the system. Without CSI, the RIS provides an array gain of N, where N is the number of reflecting elements, and user scheduling provides an multi-user gain of , where M is the number of users. With CSI, the RIS provides an array gain of , while no multi-user diversity gain can be obtained.