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Home » We want $ \mathbbE[\textoutput] $. - Nelissen Grade advocaten

We want $ \mathbbE[\textoutput] $. - Nelissen Grade advocaten

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 5**Question:** A bioengineer is working on a project to restore a wetland using genetically engineered plants that remove heavy metals from the soil. They have developed 3 types of plants: Type A, Type B, and Type C. If they plant one type in each of 5 distinct plots and repeat the plant type as needed, how many different planting arrangements can be made?

📌 Solution:** Each of the 5 plots can be planted with any one of the 3 types of plants. Thus, for each plot, there are 3 choices. The total number of arrangements is calculated by raising the number of choices to the power of the number of plots, which is \(3^5\).

📌 3^5 = 3 \times 3 \times 3 \times 3 \times 3 = 243

📌 Therefore, there are \(\boxed{243}\) different planting arrangements possible.

📌 Question:** A science fiction writer imagines a future where memories can be transferred between individuals using a neural interface. If there are 6 distinct memories to be transferred, and each memory can be either stored, shared, or discarded, in how many different ways can the files be processed?

📌 Solution:** Each of the 6 memories has 3 possible outcomes: stored, shared, or discarded. Therefore, for each memory, there are 3 choices. The total number of ways to process all memories is \(3^6\).

📌 3^6 = 3 \times 3 \times 3 \times 3 \times 3 \times 3 = 729

📌 Thus, there are \(\boxed{729}\) different ways to process the memories.

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