Expected largest of ten balls

HardCombinatorics Expected Value~8m

A box contains $20$ balls labelled $1$ through $20$ . You draw $10$ of them (without replacement). What is the expected value of the largest label among your $10$ balls?

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The $10$ picks split $\{1,\dots,20\}$ into $11$ symmetric gaps.
$\mathbb{E}[\max] = \tfrac{k(n+1)}{k+1} = \tfrac{10\cdot 21}{11}$ .

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19.0909 (± 0.01)

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Asked at: Jane Street, Two Sigma

Expected largest of ten balls

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