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Rafael is taking a test that contains a section of 12 true-false questions. How many of the possible groups of answers to these questions have at least 6 correct answers of true?

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Answer: There are 495 possible different sets of answers the could contain exactly 8 correct answers of false.

Basically, we are looking for the number of different ways of selecting 8 objects out of a set of 12 objects. Our objects are answers of false and the set is the test.

This is a combination problem. The formula would be:

12! / (8! x 4!) = 495

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