# Chapter 10.10 and 10.11

Materials

Today we focussed on two concepts:

• The complement principle - The idea that sometimes it is difficult or time consuming to calculate the number of ways a particular event happens but it is easy to calculate the number of ways that it DOESN'T happen. If you know the total number of events (the sample space) and the number of ways an event doesn't happen than

|U| - | Not Event| = | Event |

• The inclusion and exclusion principle - The idea that we have to be careful counting combinations of two different event if it is possible that BOTH events can happen together. For example, suppose that in a survey of 20 "good" students (students who get at least one A) we discover that 12 got an A in Discrete and 15 got an A in Data Structures. How can that be possible? It is only possible if 7 students got an A in BOTH classes. We discover a formula that says

| A or B | = |A| + |B| - |A and B|

Problems 26 and 42 from our worksheet are much easier to solve using the Complement Principle. Problems 35 and 39 can be solved using EITHER technique.