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1717. Empat buah dadu dilempar sekaligus. Peluang bahwa empat buah bilangan yang dihasilkan dapat disusun menjadi deret aritmatika dengan selisih 11, adalah.....\newline(A) 16\frac{1}{6}\newline(B) 112\frac{1}{12}\newline(C) 118\frac{1}{18}\newline(D) 124\frac{1}{24}\newline(E) 136\frac{1}{36}

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Q. 1717. Empat buah dadu dilempar sekaligus. Peluang bahwa empat buah bilangan yang dihasilkan dapat disusun menjadi deret aritmatika dengan selisih 11, adalah.....\newline(A) 16\frac{1}{6}\newline(B) 112\frac{1}{12}\newline(C) 118\frac{1}{18}\newline(D) 124\frac{1}{24}\newline(E) 136\frac{1}{36}
  1. Identify Sequences: Identify the possible sequences that can be formed with a common difference of 11. The smallest sequence is 1,2,3,41, 2, 3, 4 and the largest is 3,4,5,63, 4, 5, 6.
  2. Count Distinct Sequences: Count the total number of distinct sequences that can be formed. There are 33 distinct sequences: 1−2−3−41-2-3-4, 2−3−4−52-3-4-5, and 3−4−5−63-4-5-6.
  3. Calculate Arrangement Ways: Each sequence can be arranged in 4!4! (factorial of 44) ways because there are 44 numbers and we can arrange them in any order.
  4. Calculate Favorable Outcomes: Calculate the total number of favorable outcomes. Since there are 33 sequences and each can be arranged in 4!4! ways, there are 3×4!=3×24=723 \times 4! = 3 \times 24 = 72 favorable outcomes.
  5. Determine Total Outcomes: Determine the total number of possible outcomes when four dice are thrown. Each die has 66 faces, so there are 64=12966^4 = 1296 possible outcomes.
  6. Calculate Probability: Calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes. Probability = 721296.\frac{72}{1296}.
  7. Simplify Fraction: Simplify the fraction to get the final probability. Probability = 721296=118\frac{72}{1296} = \frac{1}{18}.

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