Suppose that $x_1, \dots x_n (n>2)$ are real numbers such that $x_i=-x_{n-i+1}$ for $1 \leq i \leq n$. Consider the sum $S=\Sigma \Sigma \Sigma^{x_ix_jx_k}$, where the summations are taken over all i,j,k : 1 $\leq$ i, j, k $\leq$ n and i,j,k are all distinct. Then $S$ equals
- $n! \: x_1, x_2 \dots x_n$
- (n-3)(n-4)
- (n-3)(n-4)(n-5)
- none of the foregoing expressions
