Tree DiagramsFundamental Counting Principle

Additive Counting Principle

Let’s take a Trip! We are Travelling to __________

and we have a choice of two different flights from London, England. In order to get to London from Toronto you have a choice of 3 different flights (A,B,C). But, how are you getting to the airport? (Taxi, Bus, Drive).

So, how many ways can you get there?

Each stage of the trip has multiple choices that branch off into different paths

You are making a yummy sandwich and you have a choice of white or brown bread. On your sandwich you can have only one of the following; ham, chicken or beef. To dress the sandwich you can use mustard or mayonnaise. How many different kinds of sandwiches can you make?

Total of 12 Different Sandwiches

These types of problems hold a fundamental counting principle that is multiplicative

If the problem has stages with multiple choices, then the total will be all the different choices in each stage multiplied together.

There are 2 types of BreadThere are 3 types of MeatThere are 2 types of Dressing

2x3x2 = 12

If a problem has multiple choices for different situations simply add each count together.

Also called the Rule of Sum

Sailing ships use signal flags to send messages with 4 different flags. You must use a minimum of 2 flags for each message and can’t repeat flags How many different messages are there?

You can either fly 2 flags, 3 flags or 4 flags at a time

These actions can’t happen at the same time. ( you can’t fly 2 flags and be flying 4 flags at the same time)

These events are called MUTUALLY EXCLUSIVE events. They are separate actions that can’t happen at the same time.

Sailing ships use signal flags to send messages with 4 different flags. You must use a minimum of 2 flags for each message and can’t repeat flags. How many different messages are there?

2 Flag Message 4X3 =123 Flag Message 4X3X2 = 244 Flag Message 4X3X2X1=24

Add them all together12 + 24 + 24 = 60 different possible messages

How many ways can you arrange 8 people in line for a photo? BUT Matt and Kris just broke up and can’t be beside each other

Sometimes it is easier to solve a problem indirectly. In this case we can find out how many ways it takes to put Matt and Kris beside eachother, and subtract it from the total possible matches

This is commonly called the BACK DOOR METHOD

Total Possible arrangements

Put Matt and Kris beside each other

Total arrangements – arrangements with them together = arrangements of them apart40320 -10080 =

Multiplicative Counting Principle◦ Multiply choices for each stage

Additive Counting Principle◦ Add up each mutually exclusive situation together

Back Door Method◦ Determine the opposite and subtract from total

Working with each other complete the handout given

Create a rule for the Fundamental Counting principle (multiplicative) and the Additive Counting Principle in the boxes provided

Complete the questions on the back and we will take them up in class

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