# A game of In-between

Hayley has a deck of $$x$$ cards, each labelled distinctly with an integer from 1 to $$x$$, where $$x\geq 3$$. She randomly picks 2 cards from the deck and sees that they have the numbers $$a$$ and $$b$$ written on them, where $$b>a$$. Without replacing those 2 cards, she then randomly takes another card from the deck, which has the number $$c$$ written on it.

Define the function $$p(x)$$ to be the probability that $$a<c<b$$ for a deck of $$x$$ cards. Find the value of

$\displaystyle \sum_{k=3}^{2015} {p(k)}$

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