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A system is composed of five components, each of which is either working or failed. Consider...

A system is composed of five components, each of which is either working or failed. Consider an experiment that consists of observing the status of each component, and let the outcome of the experiment be given by the vector (x1, x2, x3, x4, x5) where xi is equal to 1 if component i is working and is equal to 0 if component i has failed. Suppose that two components are working and three components have failed. In how many ways can this occur?

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