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zelda a link of the past - Anadea

📅 May 16, 2026 👤 scraface

May 16, 2026

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📌 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:

📌 So, the total number of distinct assignments is:

📌 Question: A paleobotanist is analyzing fossil plant remains from 4 distinct time periods, with 3 samples from each period. If she selects 5 samples at random, what is the probability that she selects at least one sample from each time period?

📌 Solution: The total number of ways to choose 5 samples from 12 (3 per period) is:

📌 To find the number of favorable outcomes (at least one from each of the 4 periods), we use the principle of inclusion-exclusion. Lets count the number of 5-sample selections that include at least one from each period.

📌 We subtract from the total the number of selections that miss at least one period. Lets define the total number of selections missing at least one period and subtract appropriately.

📌 Let $ A_i $ be the set of selections missing period $ i $. Then:

📌 And the full intersection is also 0.

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