# $3$ cards add up to $p$

I came up with a probability problem:

A set of $n$ cards each has a different whole number from 1 to $n$. If $3$ different cards are drawn randomly from the deck, what is the probability that the sum of the $3$ cards' values add up to $p$, where $p$ is a positive whole number and $p \leq n$?

What I have so far is the number of combinations: $$_nC_3 = \frac{n(n-1)(n-2)}{3!}$$ I know my answer will be $$\frac{(number \; of \; combinations \; that \; add \; up \; to \; p)}{_nC_3}$$

I'm not even sure if it's possible to solve, so any hints or solutions would be really helpful. Thanks in advance!

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In order to solve the number of combinations that add up to $p$, you can start by looking at en.wikipedia.org/wiki/Partition_(number_theory) and then find a way to take out the ones that have repeating numbers –  Jean-Sébastien Sep 23 '12 at 17:35
Thanks, this is exactly what I was looking for!! –  Noah Klein Sep 24 '12 at 2:42