A department manager has four employees involved with 6 projects throughout the fiscal year. In how many ways can the manager assign these projects so that each employee is working on at least one project?

Question

A department manager has four employees involved with 6 projects throughout the                  fiscal year. In how many ways can the manager assign these projects so that each employee is working on at least one project?

kropot72 · Answer

There are 6P4 ways of distributing four of the projects with one project assigned to one employee. This leaves two projects to assign for each of the 6P4 permutations. There are 4 ways of assigning these two projects to one of the employees and 4P2 ways of assigning these two projects singly to employees.
The required number of ways of assigning the projects is given by:
6P4(4 + 4P2) = you can calculate