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what's the kansas city chiefs score - Feedz API

📅 May 18, 2026 👤 scraface

May 18, 2026

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📌 A wildlife habitat specialist has 6 native birds, 4 migratory birds, and 2 endangered birds to observe. If a random sample of 5 birds is selected, how many ways are there to choose the sample such that it includes at least one bird from each category?

📌 To solve this, we use the principle of inclusion-exclusion. We need to count the number of ways to choose 5 birds including at least one from each category: native (N), migratory (M), and endangered (E).

📌 Now, subtract the cases where at least one category is missing.

📌 Now, add back the cases where two categories are missing (since they were subtracted twice):

📌 Actually, better approach: compute valid combinations directly where each category is represented.

📌 A chemical engineer is testing 12 new sustainable solvents: 5 are water-based, 4 are bio-based, and 3 are ionic. If 6 solvents are selected at random, what is the probability that at least one solvent from each type is included?

📌 We compute the probability that a random selection of 6 solvents from 12 (5 water, 4 bio, 3 ionic) contains at least one from each type.

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