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I Think We're Alone Now Film - IQnection

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 Solution: Arranging $ n $ distinguishable objects in a circle, where rotations are considered the same, results in $ (n-1)! $ distinct arrangements.

📌 Question: An angel investor is evaluating 8 early-stage tech startups and plans to fund exactly 3. If two of the startups are in AI and must either both be funded or both not funded, how many valid investment portfolios can be formed?

📌 Solution: We divide the funding decision based on the two AI startups.

📌 Let the AI startups be $ A_1 $ and $ A_2 $. The condition is: both are funded or both are not funded.

📌 Case 1: Both AI startups are funded.

📌 Then, we must choose $ 3 - 2 = 1 $ more startup from the remaining $ 8 - 2 = 6 $ non-AI startups:

📌 Then, we choose all 3 funded startups from the 6 non-AI startups:

📌 Question: A weather model uses binary sequences of length 8 to represent daily temperature anomalies (1 = above average, 0 = below). How many such sequences have at least one pair of consecutive 1s?

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