In the country of PUMaC-land, there are 5 villages and 3 cities. Vedant is building roads between the 8 settlements according to the following rules:
a) There is at most one road between any two settlements;
b) Any city has exactly three roads connected to it;
c) Any village has exactly one road connected to it;
d) Any two settlements are connected by a path of roads.
In how many ways can Vedant build the roads?