The University of Oregon’s football team has many different uniforms. The coach can choose from four colors of jerseys and pants: green, yellow, white, and black. There are three helmet options: green, white, and yellow. Also, there are the same four colors of socks and two colors of shoes, black and yellow. Use a tree diagram to find all of the possible shoe and sock combinations.
First, we can list the options for shoes:
- Black shoes
- Yellow shoes
And we can list the options for socks:
- Green socks
- Yellow socks
- White socks
- Black socks
To create a tree diagram, we start with the four options for socks at the top of the diagram:
```
Green
/ | \
Yellow | White
|
Black
```
From each sock option, we draw branches for the two shoe options:
```
Green
/ | \
Yellow | White
/\ | /\
Black Yellow Black Yellow
```
Now we can read the possible combinations from the branches:
- Green socks with black shoes
- Green socks with yellow shoes
- Yellow socks with black shoes
- Yellow socks with yellow shoes
- Yellow socks with black shoes
- Yellow socks with yellow shoes
- White socks with black shoes
- White socks with yellow shoes
- Black socks with black shoes
- Black socks with yellow shoes
- Black socks with black shoes
- Black socks with yellow shoes
In total, that's 12 possible shoe and sock combinations.