Tree Diagrams
Example 1

You are the proud inventor of the SongWriter 2000™. The user sets the song speed ("fast," "medium," or "slow"), the volume ("loud" or "quiet"), and the style ("rock" or "country"). Then, the SongWriter automatically writes a song to match. Make a tree diagram to determine how many possible settings there are.

Prob_ex4

Starting at the top of the tree and following all the way down, you end up with one particular kind of song such as, "fast loud country song." There are 12 different song types in all. The number of outcomes is found by multiplying the number of settings for each knob:
3 × 2 × 2 = 12 and is an example of the counting principle.

To learn more about the counting principle, watch the following video.