3. (12 points) Assigning 8 distinct tasks to 3 identical servers, where every task must be assigned to exactly one server.

(a) (4 points) Suppose each server can handle any number of tasks, including none. How many ways can the 8 tasks be assigned to the 3 servers with no restrictions?

(b) (2 points) Suppose that each server must handle at least one task. How many ways can the tasks be assigned?

(c) (2 points) Suppose that each server must handle at least one task, and no server can handle 5 tasks or more, how many valid task assignments are possible?

(d) (4 points) Now, consider that the servers are labeled (i.e., no longer identical), and each server must handle at least one task. Additionally, no server can handle 5 tasks or more. How many valid task assignments are there in this case?