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Home » Art John Wayne Gacy: The Master of Deception Behind Iconic American Art Pieces! - Abbey Badges

Art John Wayne Gacy: The Master of Deception Behind Iconic American Art Pieces! - Abbey Badges

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 Question: A science educator assigns 7 unique digital badgesâ3 for Robotics, 2 for Coding, and 2 for Data Scienceâto students over a week, one badge per day. If the badges within each category are indistinguishable, how many distinct daily sequences can be created?

📌 Solution: We are arranging 7 badges where 3 are identical Robotics (R), 2 are identical Coding (C), and 2 are identical Data Science (D). The number of distinct sequences is the multinomial coefficient:

📌 rac{7!}{3! \cdot 2! \cdot 2!}

📌 $ 7! = 5040 $

📌 $ 3! = 6 $, $ 2! = 2 $, so denominator = $ 6 imes 2 imes 2 = 24 $

📌 rac{5040}{24} = 210

📌 Thus, there are 210 distinct badge sequence orders.

📌 oxed{210}Question: Find all real numbers $ x $ such that $ rac{x+3}{x-2} < 4 $, where $ x

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