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Hello! My name is professor Carly and today we are going to learn about tree diagrams and the fundamental counting principle

Objectives:

• students will learn the concepts of tree diagrams and the fundamental counting principle
• students will put these concepts into practice by working through some examples

tree diagrams and the fundamental counting principle are both methods you can use to figure out the number of possible outcomes for a certain event

a tree diagram the process of drawing out every possibility.

for example:

This diagram shows every possibility for creating an outfit with the pants, shirts and shoes a person has. So one outfit combination could be blue pants, grey shirt, white shoes, another could be blue pants grey shirt and brown shoes and you continue to count the combinations following that same pattern. This is a good method to use but sometimes it can be confusing and time consuming when you begin to work with more combinations/options.

The fundamental counting principle is a much quicker way to find out the possible number of outcomes. Instead of drawing out every combination you just take the number of items within each “category” and multiply them all together. Using the example above you have:

• 2 pants options
• 3 shirt options
• 2 shoe options

Once you have those then you just multiply them together.

2 x 3 x 2= 12

So you have 12 different possible outfit combinations.

Another example could be the ice cream shop on the hill has 15 flavors, 3 types of cones and 20 different toppings to choose from. Instead of drawing a tree diagram and counting the combinations you would just multiply those numbers together to find the number of outcomes

ex: 15 x 3 x 20 = 900

• so there are 900 different ice cream combinations

so to sum up our lesson. A tree diagram is when you draw out and count every possibility and the fundamental counting principle is when you take the number of items in each category and multiply them together to get your total number of outcomes or combinations. I hope this helps you understand these concepts a little bit better