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A student must answer 10 of 12 questions on an exam. How many different choices can the student make?
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is it 66?
It depends on how you interpret the question. If the student must answer precisely 10 of 12 questions, then yes. You are counting combinations.
If he may answer more than 10 questions, then you need to do the same thing as you did with 10 of 12, but for 11 of 12 and 12 of 12 also; and then sum the three values.
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