How many ways are there to assign 5 different jobs to 4 different employees if every employee is assigned at least 1 job?

Correct option is C

We are tasked to find the number of ways to assign 5 different jobs to 4 employees such that each employee is assigned at least one job.
Key Idea:
This is a problem of distributing distinct items (jobs) into distinct groups (employees) with the condition that no group is empty. This is a variation of the surjective function problem and can be solved using the Inclusion-Exclusion Principle.
Step 1: Total ways to assign jobs without restriction
Each of the 5 jobs can be assigned to any of the 4 employees. Thus, the total ways to assign the jobs is:
45 = 1024
Step 2: Subtract invalid cases (where one or more employees receive no job)
Using the Inclusion-Exclusion Principle, we calculate:
1. Case 1: One employee gets no job