Mock AIME 2 2006-2007/Problem 13

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Problem

In his spare time, Richard Rusczyk shuffles a standard deck of 52 playing cards. He then turns the cards up one by one from the top of the deck until the third ace appears. If the expected (average) number of cards Richard will turn up is where and are relatively prime positive integers, find

Solution

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See also

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• Mock AIME 2 2006-2007

Problem Source

4everwise thought of this problem when watching Round 4 of the Professional Poker Tour. (What else can one do during the commercial breaks?)