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Question: A fair 12-sided die is rolled three times. What is the probability that the sum of the three rolls is exactly 18?
Solution: The minimum value on a 12-sided die is 1 and the maximum is 12. We want the number of integer solutions to:
Without constraints, the number of non-negative integer solutions to $ y_1 + y_2 + y_3 = 15 $ is:

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