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📅 July 6, 2026 👤 scraface

Jul 06, 2026

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📌 2Question: A micropaleontologist is analyzing microfossils from 5 different sediment layers, each layer containing a unique type of microfossil. If she selects 3 layers at random for detailed isotope analysis, what is the probability that the oldest and youngest layers are both included?

📌 Solution: To solve this, we first determine the total number of ways to choose 3 layers from the 5, which is given by the combination:

📌 Now, we want the number of favorable outcomes where both the oldest and youngest layers are among the 3 selected. If the oldest and youngest are fixed in the selection, we only need to choose 1 more layer from the remaining 3 middle layers:

📌 Question: An anthropologist is studying how 6 different cultural practices evolve over time in 4 distinct environments. If she selects 4 cultural practices and assigns each to one of the 4 environments (each environment receiving exactly one practice), how many distinct assignments are possible?

📌 Solution: First, we choose 4 out of the 6 cultural practices, which can be done in:

📌 ways. Then, we assign each selected practice to one of the 4 environments. Since each environment receives exactly one practice, this is a permutation of 4 items:

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