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📅 May 15, 2026 👤 scraface

May 15, 2026

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📌 inom{14}{2} = rac{14 \cdot 13}{2} = 91

📌 rac{91}{455} = rac{1}{5}

📌 So, the probability that the sum is even is $oxed{\dfrac{1}{5}}$.

📌 Question: Three random integers are chosen independently and uniformly from the set $\{0, 1, 2, \dots, 100\}$, inclusive. Let $z$ be the number of distinct values among the three integers. What is the probability that $z = 2$?

📌 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

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