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Home » You Won’t Believe the Classic Almost Forgotten Secrets from *The Cosby Show Series*! - Upplift

You Won’t Believe the Classic Almost Forgotten Secrets from The Cosby Show Series! - Upplift

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 We compute the probability that in 5 rolls of a fair six-sided die, exactly two distinct numbers appear.

📌 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 → \(30\)

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