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This paper addresses the problem of how to select the optimal number of sensors and how to determine their placement in a given monitored area for multimedia surveillance systems. We propose to solve this problem by obtaining a novel performance metric in terms of a probability measure for accomplishing the task as a function of set of sensors and their placement. This measure is then used to find the optimal set. The same measure can be used to analyze the degradation in system 's performance with respect to the failure of various sensors. We also build a surveillance system using the optimal set of sensors obtained based on the proposed design methodology. Experimental results show the effectiveness of the proposed design methodology in selecting the optimal set of sensors and their placement.