Calculating the volume of a $4$-simplex with edges of length $1$

Question

In the Euclidean space $(\mathbb{E}^{4})$, consider a $4$-simplex $S$ with vertices $P_{0}, P_{1}, P_{2}, P_{3}, P_{4}$. Assume that the edges of the simplex $S$ have a length of $1$.

(a) Calculate the volume of the simplex $S$.

(b) Determine the distance from the vertex $P_{4}$ to the plane $\alpha$ passing through the vertices $P_{0}, P_{1}, P_{2}, P_{3}$.