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Home » Wow—This Car Was Found Parked Oddly, and Its Story Will Shock You! - Dyverse

Wow—This Car Was Found Parked Oddly, and Its Story Will Shock You! - Dyverse

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 Solution: We are counting the number of 6-day sequences using 4 experiment types (P, C, B, A), where each type appears at least once, and sequences are ordered. This is a classic inclusion-exclusion problem: counting the number of surjective functions from a 6-day sequence to 4 experiment types.

📌 Total sequences without restriction: $ 4^6 $

📌 Subtract sequences missing at least one type:

📌 Let $ S = 4^6 $

📌 Use inclusion-exclusion:

📌 ext{Number of surjective sequences} = \sum_{k=0}^{4} (-1)^k inom{4}{k} (4 - k)^6

📌 $ k = 0 $: $ (-1)^0 inom{4}{0} \cdot 4^6 = 1 \cdot 1 \cdot 4096 = 4096 $

📌 $ k = 1 $: $ (-1)^1 inom{4}{1} \cdot 3^6 = -1 \cdot 4 \cdot 729 = -2916 $

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