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The moduli space $\overline{M}_{0,n}$ may be embedded into the product ofprojective spaces $\mathbb{P}^1\times \mathbb{P}^2\times \cdots \times\mathbb{P}^{n-3}$, using a combination of the Kapranov map$|\psi_n|:\overline{M}_{0,n}\to \mathbb{P}^{n-3}$ and the forgetful maps$\pi_i:\overline{M}_{0,i}\to \overline{M}_{0,i-1}$. We give an explicitcombinatorial formula for the multidegree of this embedding in terms of certainparking functions of height $n-3$. We use this combinatorial interpretation toshow that the total degree of the embedding (thought of as the projectivizationof its cone in $\mathbb{A}^2\times \mathbb{A}^3\cdots \times \mathbb{A}^{n-2}$)is equal to $(2(n-3)-1)!!=(2n-7)(2n-9) \cdots(5)(3)(1)$. As a consequence, wealso obtain a new combinatorial interpretation for the odd double factorial.

Projective Embeddings of $\overline{M}_{0,n}$ and Parking Functions