Suppose you have a well-shuffled standard deck of cards, (faces down). You start turning over the cards, one at a time, from the top of the deck. Let $$S$$ be the expected number of cards you need to turn over before revealing all four $$7$$'s.
If $$S = \dfrac{a}{b}$$, where $$a$$ and $$b$$ are positive coprime integers, then find $$a + b.$$