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Home » Choose which two of the three positions are odd: - AIKO, infinite ways to autonomy.

Choose which two of the three positions are odd: - AIKO, infinite ways to autonomy.

📅 May 4, 2026 👤 scraface

May 04, 2026

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Here, there are $ 5 + 3 = 8 $ people total, so:
So total number of 3-element subsets:
For $ a = 0 $ to $ 19 $: $ b $ from $ a+1 $ to $ 40 - a $
For $ a = 20 $ to $ 40 $: $ 40 - a < a $, so no such $ b $
For $ a > 40 $: $ a + b > 40 $, so excluded
Better: $ b $ from $ a+1 $ to $ 40 - a $, so $ k = 50 - b $ from $ 50...
This is messy. Instead, compute numerically.
Let $ d = b - a $, so $ d = 1 $ to $ 40 - 2a $
So total number of favorable triples:
So even sum: $ 10500 - 5740 = 4750 $

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