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The authors perform an outage probability analysis of a cooperative communication system which transmits over multi-path channels with best single, or best two relay pair selection and amplify-and-forward two-hop relaying. The probability density function of the multi-path links is modelled in the time domain with an Erlang distribution function. The analytical expressions for the probability density function and cumulative density function of the end-to-end signal-to-noise ratio are obtained for an arbitrary number of relay nodes and multi-path channel lengths of 2 and 3 with best single and best two relay pair selection from N available relays; from which outage probabilities are calculated. The spatial and temporal cooperative diversity of the network is then analysed. Finally, the theoretical results are compared with simulations to confirm the validity of the analysis, and the advantage of two relay selection is verified through bit error rate evaluation.