Which mode of file permissions provides a way to specify settings using both letters and symbols?

The mode of file permissions known as symbolic mode allows you to specify settings using both letters and symbols. In this context, 'symbolic mode' utilizes a combination of letters that represent the user categories—owner, group, and others—and actions like read (r), write (w), and execute (x). Additionally, symbolic notation allows for the use of operators such as '+' to add permissions, '-' to remove them, and '=' to set specific permissions.

This mode is particularly useful for making changes to permissions on a per-user basis without needing to understand numerical equivalents. For instance, using a command like chmod g+w file.txt modifies the permission for the group to include write access, showcasing the clarity and flexibility that symbolic mode offers.

In contrast, absolute mode refers to a numerical representation of permission settings, which does not involve letters or symbols in the same way. Binary mode is not a recognized standard terminology for file permissions in Linux, and octal mode, while similar to absolute mode, employs numismatic values to define permissions rather than the symbolic representation. The correct answer highlights the unique advantage of symbolic mode in providing an intuitive way to manage file permissions in a descriptive manner.