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Combinatorics Principles: Rules of Sum and Product

Combinatorics Principles: Rules of Sum and Product

Author: c o

To introduce the principle of sum
To introduce the principle of product
To apply these principles to the problem of determining the total number of subsets of a set

In this packet we learn about the combinatorial principle of sum and of product and we see examples of their application.

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Background And Introduction

Before starting with this lesson, you should be familiar with basic set theory and with the notion of combinations and permutations.


When a number of different events have the possibility of happening, some in conjunction, and some in mutual exclusion, keeping track of the bigger picture can be a challenge.  Part of understanding this "bigger picture" often involves knowing how many different arrangements of events are possible, so that each one can be examined in turn.

In this lesson we investigate two fundamental principles for taking such an account.

Motivating The Rules - Planning A Weekend

This video uses an example about making plans for the weekend to motivate the concepts central to this packet.

Counting Subsets

We apply the rule of product and the rule of sum to count the number of total possible subsets of a set with n elements, and use these two differenct counts to establish a useful identity.