The monitoring of power distribution networks and identification of system faults become more and more important as the overall power grid undergoes structural changes. Such changes are due to the increasing integration of distributed and volatile renewable generation units. This work focuses on strategies for the placement of phasor measurement units (PMU) in a power distribution system, such that the detection and classification of line outages can be facilitated accurately.The determination of sensor locations is based on a feature selection approach, where the measurement locations, which provide the most informative input to the supervised learning techniques, are successively selected until the required classification accuracy is obtained. Hence, the number of required PMUs is minimized without jeopardizing the detection accuracy. The proposed methodology is applied to benchmark distribution systems, where simulated data is used for training deep neural networks (DNN), decision trees (DT), and random forests (RF) for fault detection and classification.