30. Volume of the Simplex

Let $S_n$ be an $n$-dimensional simplex whose edges from one vertex are $v_1,v_2,\ldots,v_n$, and let $P_n$ be the parallelepiped generated by these same vectors.

Prove that the volume of $S_n$ is exactly $\frac{1}{n!}$ of the volume of $P_n$ and hence derive the closed form formula of $S_n$.