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what time are the football games tonight - ClickBalance

📅 May 18, 2026 👤 scraface

May 18, 2026

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📌 So split into cases based on whether layer 1 is in the selected set.

📌 For each such triple (includes 3, excludes 1), number of permutations: $3! = 6$

📌 In each of these, layer 3 is in the sequence, and since 1 is absent, the condition 3 appears before 1 is vacuously true.

📌 In any permutation of 3 distinct elements, in exactly half the orderings, 3 comes before 1.

📌 Now, total favorable sequences: $18 + 9 = 27$

📌 Total possible sequences with layer 3: 36 (from earlier)

📌 Wait: number of sequences containing both 3 and 1:

📌 Then sequences with 3 not with 1: 36 - 9 = 27, all satisfying condition (since 1 not present

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