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Home » z^5 + z^3 + z + 1 = z^3(z^2 + 1) + 1(z + 1). - Portal da AcÃºstica

z^5 + z^3 + z + 1 = z^3(z^2 + 1) + 1(z + 1). - Portal da AcÃºstica

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 rac{12!}{5! \cdot 4! \cdot 3!} = rac{479001600}{120 \cdot 24 \cdot 6} = rac{479001600}{17280} = 27720

📌 Now compute the product of probabilities:

📌 \cdot 0.000002238 pprox 0.0622

📌 Thus, the probability is approximately $ oxed{0.0622} $.

📌 Question: A museum curator is digitizing a collection of 10 rare scientific instruments, each with a unique provenance history. If the curator selects 4 instruments at random to feature in a virtual exhibit, what is the probability that a specific instrument, known to be historically significant, is among them?

📌 Solution: The total number of ways to choose 4 instruments from 10 is:

📌 inom{10}{4} = 210

📌 To count favorable outcomes (the significant instrument is selected), we fix one of the 4 spots to be occupied by the significant instrument, and choose the remaining 3 from the remaining 9:

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