QC is an activity that verifies whether or not the product produced meets standards. QA is an activity that establishes and evaluates the processes that produce the products. If there is no process, there is no role for QA.
QA would determine the need for, and acquire or assist in the installation of development methodologies, estimation processes, system maintenance processes, and so forth. Once installed, QA would measure them to find weaknesses in the process and then correct those weaknesses to continually improve the processes.
It is possible to have quality control without quality assurance. For example, there might be a standard that “ALTER GO TO” statements in COBOL should not be used. Regardless of whether a program is produced using a system development process or done by an individual without a process, it could still be checked to determine whether or not “ALTER GO TOs” are in the program.