Chapter 1 – Counting Techniques

Chapter 1 introduces students to counting techniques necessary for the study of probability. How many outcomes are possible when rolling two dice? when flipping four coins? when drawing five cards from a deck of 52? The basic building block is the General Counting Principle, from which Permutations are a specific application. The connection between Permutations and Combinations is developed, as well as the connection between Binary models (coin flips) and Combinations.

Seeing the interconnectedness of these topics is important for success in probability and students should be encouraged to focus on the similarities between topics. For example, why is the formula for combinations the same as the formula for permutations with an extra factor in the denominator? What is the extra factor? What does it represent?

The lesson on Permutations is presented in two parts. Part I follows the General Counting Principle and places ALL members of a set in order. Part II does the generalization when only some of the members are placed in order.