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Home » Free & Addictive: Play These Hyper-Addictive Online Multiplayer Games Tonight! - ClickBalance

Free & Addictive: Play These Hyper-Addictive Online Multiplayer Games Tonight! - ClickBalance

📅 May 18, 2026 👤 scraface

May 18, 2026

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📌 Therefore, \( R(x) \) approaches \(-2\) as \( x o 1 \), but it is undefined at \( x = 1 \).

📌 The function is undefined at \( oxed{x = 1} \), with a limit of \(-2\) as \( x o 1 \).

📌 ---Question: A museum curator is organizing a digital exhibit featuring 8 historical telescopes and 5 early microscopes. If the exhibit layout requires selecting 3 telescopes and 2 microscopes to display in a row, how many distinct arrangements are possible?

📌 Solution: We are selecting and arranging instruments for display. First, choose 3 telescopes from 8: $inom{8}{3}$. Then, choose 2 microscopes from 5: $inom{5}{2}$. After selection, arrange the 5 chosen instruments in a row: $5!$ ways.

📌 inom{8}{3} = rac{8 \cdot 7 \cdot 6}{3 \cdot 2 \cdot 1} = 56

📌 inom{5}{2} = rac{5 \cdot 4}{2 \cdot 1} = 10

📌 Total arrangements: $56 \cdot 10 \cdot 120 = 67200$.

📌 Thus, the number of distinct arrangements is $oxed{67200}$.

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