Twelve cities are divided into 3 Zones of 4 cities. Telephone Department intends to connect the cities with telephone lines such that every two cities in the same zone are connected with three direct lines and every two cities belonging to different zones are connected with two direct lines. How many direct lines are required?
I have the first part figured out. Within one zone, two cities can be connected three direct lines. Since there are 4 cities in one zone, two of them can be connected in $\binom42$ ways. There are three zones and two direct links are needed. Hence, $$3×\binom42×2$$ I have no idea on how to solve the second part.