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Home » y = 2\left(\frac43\right) + 3 = \frac83 + 3 = \frac83 + \frac93 = \frac173 - Dachbleche24

y = 2\left(\frac43\right) + 3 = \frac83 + 3 = \frac83 + \frac93 = \frac173 - Dachbleche24

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 Step 1: Total possible outcomes:

📌 6^5 = 7776

📌 Step 2: Count favorable outcomes — sequences of 5 rolls using exactly two distinct values.

📌 Choose 2 distinct values from 6: \(\binom{6}{2} = 15\)

📌 For each pair (say \(a, b\)), count the number of 5-length sequences using only \(a\) and \(b\), excluding the all-\(a\) and all-\(b\) cases (since we need both to appear at least once).

📌 Number of binary sequences of length 5 with two values: \(2^5 = 32\)

📌 Subtract 2 constant sequences → \(30\)

📌 So for each pair, 30 valid sequences.

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