What is the difference between a mutex and a semaphore?

Question $10$ options:

A mutex allows only one process to access a shared resource at a time, while a semaphore can allow multiple processes to access the resource at the same time.

A mutex can be used for both mutual exclusion and synchronization, while a semaphore is used only for synchronization.

A mutex is a binary semaphore, while a semaphore can have any positive integer value.

There is no difference between a mutex and a semaphore.