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Outage probability analysis of a multi-path cooperative communication system with single relay selection and amplify-and-forward (AF) relaying is addressed. In this work, the probability density function (PDF) of the multi-path and two-hop wireless transmission is modeled in the time domain as an Erlang distribution function. As a result of this model, the outage probability of the multi-path fading channels is theoretically calculated for selecting one from N relays. Moreover, the analytical expressions for the PDF and cumulative density function (CDF) of the end-to-end signal-to-noise ratio (SNR) are obtained. Finally, the theoretical results are compared with simulated results to confirm the validity of the analysis.