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Home » From Charming Characters to Cozy Vibes: The Cute Games You Cant Miss! - Feedz API

From Charming Characters to Cozy Vibes: The Cute Games You Cant Miss! - Feedz API

📅 May 20, 2026 👤 scraface

May 20, 2026

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📌 The probability that both selected zones are in the same work area is $\boxed{\frac{1}{11}}$.

📌 Question: A digital health system uses a 5-character verification code composed of uppercase letters (A–Z) and digits (0–9), where the first character must be a letter, and no character is repeated. How many valid verification codes are possible?

📌 Solution: The code starts with a letter, so there are 26 choices for the first character. For the remaining 4 characters, we choose from the remaining $25 + 10 = 35$ characters (since one letter has already been used), with no repetition:

📌 \times P(35, 4) = 26 \times \frac{35!}{(35 - 4)!} = 26 \times \frac{35!}{31!}

📌 \times 34 \times 33 \times 32 = 125Point6120

📌 \times 1256120 = 32665920

📌 Thus, the total number of valid verification codes is $\boxed{32665920}$.

📌 Question: An industrial hygienist is evaluating air quality data from 8 monitoring stations arranged in a ring around a factory. If 3 stations are randomly selected for calibration, what is the probability that no two selected stations are adjacent on the ring?

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