Final answer:
The octal representation of the permissions -rwxr-sr- would be 2764, but the closest answer given is 2766, indicating a possible error in the options provided.
Step-by-step explanation:
The permissions -rwxr-sr- in the octal expression indicates the access rights on a Unix or Linux system for a specific file or directory. In the octal numbering system, read (r), write (w), and execute (x) permissions are represented by the numbers 4, 2, and 1 respectively. The presence of the permissions is added together to form the octal number for each of the three groups (owner, group, others).
Breaking down the permissions:
-rwx: The owner has all permissions (read, write, execute), which is represented by the number 7 (4+2+1).
r-s: The group has read and execute permissions with the setuid bit set (indicated as 's' instead of 'x'), which is represented by the number 6 (4+0+2).
r--: Everyone else has read permissions only, represented by the number 4 (4+0+0).
The complete octal representation of these permissions is therefore 2764. Hence, the correct answer is option 2) 2766 which likely accounted for an error in the octal value provided in the question as 's' for setuid should not add into the permission's arithmetic as a regular execute bit would.