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Teachers & SchoolsStudy Guide

Let’s say we’re making an intro for our YouTube movies. Using an online template we have 3 song choices that sync with the template, 4 different colors we can use for our text, and 2 background graphics. How many choices do we have in all?

There are 3 songs to choose from: Jazzel, Funkadoor, and Pipesong. The 4 colors are neon green, silver, banana yellow, and cobalt. Finally, we can either have stars as our background graphics, or swirls. Let’s make a chart to see all of the possible intros. Starting with song choice we get:

No matter which song we pick, we now have 4 colors to choose from.

For each of the 4 colors, we have 2 graphics to choose from.

Counting up each final branch on the tree diagram, we see there are 24 possible video intros we can make. Our favorite is Funkadoor, cobalt, swirls.

But if the question is just, “how many different intros can we make?” then the answer is simple to find. We can multiply the number of options for each choice and that gives us the total number of outcomes. So we can multiply 3 × 4 × 2 and see that there are 24 different outcomes. This is called the Counting Principle.

**Basic counting principle:** to find the total possible outcomes for two or more events, simply multiply the possible outcomes for each event together

**Total Outcomes = # of outcomes for event 1 × # of outcomes for event 2 × # of outcomes for event 3, and so on…**