Which of the following departments is NOT outside of the Department of Homeland Security?

The appropriate department that is not part of the Department of Homeland Security is the Department of Education. The Department of Homeland Security (DHS) focuses on various issues related to public safety, immigration, border security, and emergency management, among others. The Department of Education, in contrast, is solely dedicated to policies and regulations that govern education in the United States.

The other departments mentioned—Labor, Justice, and State—are all separate entities with distinct roles. The Department of Labor deals with workforce issues, the Department of Justice focuses on law enforcement and legal matters, and the Department of State manages international affairs and diplomacy. Each of these operates independently of the DHS, which is why the Department of Education stands out as the option that, while not related to national security or immigration, also does not fall under the umbrella of the Department of Homeland Security.