On a Complete Graph with N Vertices, There Are N!/2

Multiple Choice

On a complete graph with n vertices, there are n!/2 Hamilton circuits starting at a given vertex, not counting reverse routes. If a traveling salesman wanted to make deliveries to nine cities in a region, how many possible routes would he have to check to find the shortest one?

A) 2520
B) 20,160
C) 181,440
D) 1,814,400