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HMMT 2023 U4

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A standard nn-sided die has nn sides labeled 1 to nn. Luis, Luke, and Sean play a game in which they roll a fair standard 4 -sided die, a fair standard 6 -sided die, and a fair standard 8 -sided die, respectively. They lose the game if Luis's roll is less than Luke's roll, and Luke's roll is less than Sean's roll. Compute the probability that they lose the game.

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{1}{4}

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