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Home » Discover the Absolute Best Pokémon Games You Need to Play Now! - ECD Germany

Discover the Absolute Best Pokémon Games You Need to Play Now! - ECD Germany

📅 May 15, 2026 👤 scraface

May 15, 2026

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📌 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.

📌 Thus, the number of favorable selections is:

📌 Question: A micropaleontologist has 5 vials containing samples from 3 different geological eras: 2 from Era A, 2 from Era B, and 1 from Era C. If she selects 3 vials at random, what is the probability that all 3 vials are from different eras?

📌 Solution: Total number of ways to choose 3 vials from 5 is:

📌 To have all 3 from different eras, we must pick 1 from Era A, 1 from Era B, and 1 from Era C. There are:

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