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?

For a group with exactly k answers marked true, there are C(12, k) ways to choose those questions. Count groups with 6 through 12 true answers: C(12,6) + C(12,7) + … + C(12,12) = 2510. The correct choice is 2510.

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