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An admission test given by a university contains 12 true-false questions. Nine or more of the questions must be answered correctly in order to be

An admission test given by a university contains 12 true-false questions. Nine or more of the questions must be answered correctly in order to be admitted.

a. How many different ways can the answer sheet be filled out?

b. How many different ways can the answer sheet be filled out so that 9 or more questions are

answered correctly?

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