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📅 May 14, 2026 👤 scraface

May 14, 2026

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📌 First, compute $ P(F) $: the probability that at least one of A or B is in the trio.

📌 Thus, the number of 3-element subsets containing X and at least one of A or B is:

📌 We now count how many of these satisfy:

📌 $ a < b < c $ — strictly increasing order (one compound choice),

📌 But since $ a < b < c $, we have $ b - a > 0 $, $ c - b > 0 $, so:

📌 We list all such triplets and count how many satisfy $ 2b < a + c $.

📌 Lets proceed systematically. For each combination, compute $ a, b, c $, check $ 2b < a + c $.

📌 We can fix $ b $, then $ a < b $, $ c > b $, and search.

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