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Home » $24 = 2^3 imes 3$, - Groen Casting

$24 = 2^3 imes 3$, - Groen Casting

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 A technology company has developed a new AI algorithm and filed 5 patent applications. Each application can be filed in 3 different jurisdictions. In how many ways can they file all their patent applications?

📌 To solve this, we need to determine the number of ways to file 5 applications across 3 jurisdictions, where each application can be filed independently in any of the 3 jurisdictions. This is calculated as \(3^5\).

📌 An angel investor is evaluating 6 startups and plans to invest in 3 of them. In how many different ways can the investor choose which startups to invest in?

📌 This problem is a combination problem where we choose 3 startups from 6. The number of ways is given by \(\binom{6}{3}\).

📌 \binom{6}{3} = \frac{6 \times 5 \times 4}{3 \times 2 \times 1} = 20

📌 A patent lawyer is reviewing 4 patent documents, each containing 5 claims. If he reviews one claim per hour, how many hours will it take to review all claims?

📌 Each document has 5 claims, and there are 4 documents, resulting in a total of \(4 \times 5 = 20\) claims. At one claim per hour, it will take 20 hours.

📌 A STEM enthusiast is exploring binary code and learns that a 4-bit binary number can represent 16 different values. What is the total number of different 4-bit binary numbers possible?

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