Question

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

Answer 1

Answer:

1)selection

2)recruitment

3) job consultancy

4)advertisment

5)direct interview

Explanation:

Answer 2

Answer:

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

The answer uses the Principle of Inclusion and Exclusion and is 1800.

And this does not agrees with my intuition.

My intuition was that to first ensure that every employee is assigned at least a job, one job must be assigned to each employee initially, which then there will be one job left.

So, (65)⋅5! many ways to do it.

The one job left can then be assigned to any of the five employees.

So 5 ways to do it.

Finally, by rule of product, there is a total of (65)⋅5!⋅5=3600 ways.

And this does not agree with the model answer 1800.