# Do you expect this?

In his spare time, Ricky 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 Ricky will turn up is $$\dfrac{m}{n}$$, where $$m$$ and $$n$$ are relatively prime positive integers, find $$m+n$$ .

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