An important function of county government is running elections. Option C is correct.
In the United States, an administrative or political subdivision of a state is a county, which is a region with specific boundaries and some level of governmental authority. The particulat governmental powers of counties is different between the states. The powers of counties derive from state law and vary widely.
Counties tend to be governed by an elected body, called the county commission, board of supervisors, commissioners' court, county council, board of chosen freeholders, county court, or county Legislature.