Final answer:
Different methods of filling public offices at different levels of government include election, appointment, and lottery or sortition.
Step-by-step explanation:
When it comes to filling public offices at different levels of government, there are different methods that are used. One method is election, where individuals are chosen through a voting process. This is commonly used for positions like the president of the United States or members of Congress. Another method is appointment, where individuals are selected by someone in power, such as a governor or mayor. This is often used for positions that require specific expertise. Lastly, there is the method of lottery or sortition, where individuals are chosen randomly to fill public roles. This method was historically used in ancient Greece to prevent corruption and patronage.