Advanced Math Student Directions
Text  Counting and Probability 2nd edition by David Patrick
published by The Art of Problem Solving (2008)
You can find a lot of interesting ideas and videos at the Art of Problem Solving (AOPS) website  www.artofproblemsolving.com)
A link to various chapters of Richard Ruszcyk's videos on Counting can be found at:
http://www.artofproblemsolving.com/Videos/index.php?  click on the third little diamond down.
A link to various chapters of Richard Ruszcyk's videos on Counting can be found at:
http://www.artofproblemsolving.com/Videos/index.php?  click on the third little diamond down.

Counting Lists Richard Rusczyk  founder of the Art of Problem Solving company 

Using Venn Diagrams
Venn diagrams with two circles in a rectangle. The second example uses a variable and an equation to work out the solution. Count everything once and only once. Venn diagrams using three intersecting circles. This video introduces the Principle of Inclusion  Exclusion (PIE). This Principle is not given in the Chapter 1 text. 

Counting IndependentlyHere we begin to see ways to carefully count a collection of events. Dr. Ruszcyk show us a Tree Diagram technique to get started. The Chapter 1 text by Patrick also shows us a Grid method. The second video can get a little tedious, but does have a message at the end. 

Two more videos for Chapter 1 work. Here we get into Factorials  n!


Let's try some Permutations!
Part 1 

More on Permutations
(with notation) Part 2 

A Bonus! Welcome to the Liars Club!
Counting With and Without Replacement 