# A pair or two ....

A well-shuffled, standard 52-card deck is dealt out into $$26$$ piles of $$2$$ cards per pile. The expected number of piles that consist of pairs is $$\dfrac{a}{b}$$, where $$a$$ and $$b$$ are coprime positive integers. Find $$a + b$$.

Clarification: By "consists of pairs" I mean that a pile consists of two cards of the same denomination, i.e., a pair of Jacks, a pair of $$6$$'s, etc..

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