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Home » d^2 = 25 \\ - AIKO, infinite ways to autonomy.

d^2 = 25 \\ - AIKO, infinite ways to autonomy.

📅 May 2, 2026 👤 scraface

May 02, 2026

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📌 An AI analyst in Washington, D.C. is training a fairness-aware machine learning model and must select a diverse test dataset. She chooses 5 participants from 3 demographic groups: 8 from Group A, 6 from Group B, and 4 from Group C. What is the probability that her selection includes at least one participant from each group?

📌 We compute the number of favorable outcomes: selections with at least one from each group. Use complementary counting: subtract cases missing at least one group.

📌 So subtract only the pair involving Group C: 56

📌 Wait — correction: when we subtract the single exclusions, we over-subtract the double exclusions, which are zero, so no need to add back.

📌 Check if further reduction: GCD(2791,4284). Use Euclidean algorithm:

📌 But better to compute decimal or leave as reduced? Its already simplified.

📌 But this seems messy. Lets double-check inclusion-exclusion:

📌 Integer partitions of 5 into 4 positive integers: only (2,1,1,1) and permutations.

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