If you are really interested in learning counting and probability techniques, I would recommend this book:

*Introduction to Counting and Probability* by David Patrick

This book is available through the Art of Problem Solving web site, which is a great resource in itself. They also have free videos to accompany each chapter of this book posted here.

I have to admit, when I was in high school, I learned the formulas for permutations and combinations long enough to get through the test, but I never felt comfortable with the subject. I never really understood it, so once the test was over, I promptly forgot it all. It wasn’t until I went through the subject with my son a few years ago using David Patrick’s book that I finally felt like I really understood it. He says over and over in his book, “Don’t memorize! Understand, and know.” And once you understand, these problems actually become fun! It’s the best introduction to the subject that I know of. It’s extremely well written and has a solutions manual, so it’s perfect for self-study.

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