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Expected number of prize winners after dealing cards twice

Source: Japanese MO Finals 1994

February 11, 2011
countingdistinguishabilityprobabilityexpected valuecombinatorics proposedcombinatorics

Problem Statement

In a deck of NN cards, the cards are denoted by 11 to NN. These cards are dealt to NN people twice. A person XX wins a prize if there is no person YY who got a card with a smaller number than XX both times. Determine the expected number of prize winners.
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