Graphs and NetworksSalesman
In a graph with
This means that, in total, there are ${tsnPaths(tsn1)} possible paths. A shorthand for this product is ${tsn1}! or ${tsn1} Factorial.
You could imagine that it might not be possible to travel directly between two cities - without going via another city. In that case we no longer have a complete graph, and finding the number of Hamiltonian cycles, if they exist at all, becomes much more difficult.