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Suppose that the probabilities are 0.60, 0.20, 0.10, and 0.10 that a state income tax return will be filled out correctly, that it will contain only errors favoring the taxpayer, that it will contain only errors favoring the state, or that it will contain both kinds of errors. What is the probability that among 12 such income tax returns randomly chosen for audit, 5 will be filled out correctly, 4 will contain only errors favoring the taxpayer, 2 will contain only errors favoring the state, and 1 will contain both kinds of errors?

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