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Solution: The total number of distinct rankings is calculated by treating the - go-checkin.com

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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\mathbb{E}[\text{output}] = \sum_{k=0}^{3} (8 - k) \cdot \frac{\binom{...
Compute each sum.
First sum ($k = 0$ to $3$):
$ (8-0)\binom{8}{0} = 8 \cdot 1 = 8 $
$ (8-1)\binom{8}{1} = 7 \cdot 8 = 56 $
$ (8-2)\binom{8}{2} = 6 \cdot 28 = 168 $
$ (8-3)\binom{8}{3} = 5 \cdot 56 = 280 $
Total = $8 + 56 + 168 + 280 = 512$
Second sum ($k = 4$ to $8$):
$4\binom{8}{4} = 4 \cdot 70 = 280$

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