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You Wont Believe This Hidden Feature - Network4

📅 May 18, 2026 👤 scraface

May 18, 2026

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📌 Solution: We compute the probability that exactly two distinct values appear among the three chosen integers.

📌 Total number of possible outcomes: $101^3$, since each integer has 101 choices.

📌 Now, count favorable outcomes where exactly two distinct values occur.

📌 Step 1: Choose the two distinct values. Let them be $a$ and $b$, $a

📌 e b$. There are $inom{101}{2}$ ways to choose the pair.

📌 Step 2: For each such pair, how many ways can the three integers be assigned to $a$ and $b$ such that both appear at least once?

📌 The total assignments: $2^3 = 8$, but subtract the 2 cases where all are $a$ or all are $b$. So $8 - 2 = 6$ valid binary strings with both values present.

📌 Thus, number of favorable outcomes:

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