Final answer:
The Social Security Administration is responsible for determining Medicare eligibility and processing premium payments, not the Centers for Medicare & Medicaid Services, which manages the program (option c).
Step-by-step explanation:
The group that determines whether someone is eligible for Medicare and processes their premium payments is c. The Social Security Administration (SSA). The SSA is tasked with overseeing the application process for Medicare and managing the collection of premium payments from enrollees.
While Medicare is offered mainly to individuals over 65 years old, the Centers for Medicare & Medicaid Services (CMS) handle the administration of the Medicare program itself, including policy-making and direct oversight.