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Home » \[ 0.2m \leq 100 \] - Moon Smoking

\[ 0.2m \leq 100 \] - Moon Smoking

📅 May 14, 2026 👤 scraface

May 14, 2026

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📌 So, the total number of arrangements is:

📌 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:

📌 Now subtract the number of invalid solutions where one or more $ y_i > 11 $.

📌 There are 3 such cases (one for each variable), so total invalid cases:

📌 This has no non-negative solutions. So no such cases.

📌 Total possible outcomes when rolling a 12-sided die 3 times:

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