I've come across a combinatorics problem where I'm fairly certain that a solution exists, yet I'm unable to find it.
I'm trying to find the number of vectors $(x_1,x_2,...,x_n)$ such that
$\sum x_i = 0 \mod P$ for some sufficiently large prime $P$ (i.e the resulting formula should hold for all but some finite number of $P$) and
$x_i \neq x_j, \ 1 \leq i < j \leq n$.
The answer should be $(p-1)(p-2)...(p-n+1)$. What I would like to do is find a combinatorial proof of the number of partitions. However, I'm stumped.