Question 907908
You gave us a lot information but there is no question.

A, B, C, D, and E. She interviewed eight people and concluded the following: Applicant 1 can work in departments A, D and E,
 Applicant 2 can work in departments A, B, and C, 
Applicant 3 can work in departments B and E,
 Applicant 4 can work in department C only, 
Applicant 5 can work in departments B and D, and 
Applicant 6 can work in departments B, C and D, 
Applicant 7 can work in departments C and E,
 and Applicant 8 can work in any department.

One selection is:
Start with the most restrictive
 
Applicant 4 can work in department C only,
Applicant 7 can work in departments C and E, C is taken so he goes in E
Applicant 3 can work in departments B and E, E is taken so he goes in B
Now we need A and D
Applicant 2 can work in departments A, B, and C,b and C are taken so he goes in A

D is left
#5 can go in D
#8 can go in D
#6 can go in D
#1 can go in D
There are 8 applicants for 5 positions. You can't hire all of them