Question

For a custom car, there are 7 choices of wheel covers, 4 choices of stereos, 8 choices of colors, and 2 choices of windows. If you made a tree diagram to show all the possible outcomes, how many leaves would the tree diagram have?

Answer 1

`4xx2xx7xx8=448`

Explanation:

Let's first look at 2 categories of choices then expand on that.

We have 2 choices of windows - let's say "clear" and "tinted". We also have 4 choices of stereo - let's say HiFi, CD, HDMI, and AMFM.

For each choice of stereo, we can have either clear or tinted windows. There's 4 choices of stereo and 2 choices each of windows, so that's `4xx2=8`

We can expand this to the other two categories of choices as well, the 7 types of wheel cover and the 8 different colour choices. We'll multiply these in and end up with:

`4xx2xx7xx8=448` different combinations of choices we can make, which is the number of leaves on the tree diagram.