Eulerian and Hamiltonian Graphs · Hard problem

The Petersen graph has $10$ vertices with an outer $5$-cycle, inner pentagram, and spokes connecting corresponding vertices. Consider two adjacent vertices in the graph, say $0$ and $1$ (which are neighbors in the outer $5$-cycle). How many Hamiltonian paths exist that start at $0$, visit all other $8$ vertices exactly once, and end at $1$?