How many ways are there to assign six jobs to five different

How many ways are there to assign six jobs to five different employees if every employee is assigned at least one job?

Solution

Answer:

Since each employee is assigned at least one job and there are five employees and the number of jobs are six which is just one more than the umber of employees. So that means exactly 1 employee will be assigned two jobs and other four employees are assigned exactly one job. Since the employee who will be assigned 2 jobs could be any of the five employees so the number of ways in which this can be done is equal to

( 6 x 5 x 4 x 3 x 2 ) x 5 = 3600

Hence there are 3600 ways to assign six diferent jobs to five employees if each employees is assign at least one job.