In the Spring of 2015 I taught a course on Applied Combinatorics, using a superb book by Alan Tucker.
You will find the outline of the course by following this link:
The interesting feature of the course is that about a half is spent on Graph Theory, and the other half is
devoted to classical Enumeration Methods, and interesting topics which combine Graph Theory and Enumeration Methods.
The course culminates in the study of Rook Polynomials, which is a method to solve the assignment problem.
I hope my students enjoyed the course as much as I did teaching it!