There are 9 US Post Offices in Carbon County serving a total of 9,577 residents equating to 1,064 residents per post office. It's estimated that approximately 15,286 packages are handled across the 9 county post offices annually. Carbon County is a county located in the U.S. state of Montana. As of the 2010 census, the population was 10,078. Its county seat is Red Lodge. Carbon County is part of the Billings, MT Metropolitan Statistical Area."