Question

How many ways are there to assign six different jobs to three different employees if the hardest job is assigned to the most experienced employee and the easiest job is assigned to the least experienced employee?

Short answer

Number of ways to assign six different jobs to three different employees is \(65\) such that the hardest job is assigned to the most experience employee and easiest job is the least experienced employee

Step-by-step solution

In the problem given

Total number of different jobs assigned to three different employees such that the hardest job is assigned to the most experience employee and easiest job is the least experienced employee.

The definition and the formula for the given problem

Which means we have no choice for assign easiest and hardest job to the three employees and remaining four jobs can be assigned three employees in\({3^4}\)ways.

If each employee has to be assigned at least one job, this means that the third employee must have at least one job which is easiest and the other\(2\)employees can have assign remaining\(4\)jobs in\({2^4}\)ways.

Determining the sum in expanded form

Hence, the total number of employeeshas to be assigned at least one job is \(\begin{array}{c}{3^4} - {2^4} = 81 - 16\\ = 65\end{array}\)

Thus, number of ways to assign six different jobs to three different employees is \(65\) such that the hardest job is assigned to the most experience employee and easiest job is the least experienced employee