There are 7 US Post Offices in Randolph County serving a total of 18,498 residents equating to 2,643 residents per post office. It's estimated that approximately 29,525 packages are handled across the 7 county post offices annually. Randolph County is a county located in the U.S. state of Arkansas. As of the 2010 census, the population was 17,969. The county seat is Pocahontas. Randolph County is Arkansas's 32nd county, formed on October 29, 1835, and named for John Randolph, a U.S. senator from Virginia, who was influential in obtaining congressional approval of the Louisiana Purchase, of which Randolph County is a part. Randolph County is currently an alcohol prohibition or dry county."