Sample Spaces, Tree Diagrams, and the Counting Principle

What information does a tree diagram provide?

• Average Results

• Consistency Correlations

• Directional Distribution Counts

• Possible Outcomes

A native flowering plant has several varieties. The color of the flower can be red, yellow, or white. The stems can be long or short and the leaves can be thorny, smooth, or velvety. How many variations can there be?

• 8

• 18

• 21

• 27

If Eduardo flipped a coin three times, his sample space of results would contain how many variations. Remember that order matters.

• 4

• 8

• 12

• 14

In Billy's sock drawer, he has loose socks of three colors (red, white and brown). If he reaches in twice, what is the total possible of combinations he could grab?

• 3

• 6

• 9

• 12

During snack time, the students were offered their choice of either white or chocolate milk, and either chocolate chip or oatmeal cookies. How many variations were possible?

• 1

• 2

• 4

• 6

For the upcoming semester at college, Lyric has to select one literature course and her choices are world literature, American literature or British literature. She'll also have to select a history class that either focus of ancient history, U.S. history or modern history. She's also picking between four physical education classes - golf, racquetball, bowling or swimming. If she made a tree diagram to show all the possible combinations, how many different possibilities would there be?

• 10

• 13

• 27

• 36

Spencer has an eight-sided die that is marked from 1 to 8. if he rolls it twice, how many number combinations would be possible?

• 8

• 16

• 64

• 80

If Alonzo orders a cheeseburger, he first must decide if he wants a single patty or a double. Then, he has to choose either cheddar cheese, Swiss cheese or pepper jack cheese. Finally, he has to pick mayonnaise or mustard. If he created a tree diagram for his choices, how many different variations would there be available?

• 7

• 12

• 19

• 24

How many outfits are possible with 5 pairs of jeans, 8 t-shirts, and 2 pairs of shoes?

• 15
• 40
• 80
• 10

How many styles of sneakers are possible if Jared can choose from high-top or low-top, shoelaces or velcro, and the colors black, white, and red?

• 12
• 7
• 223
• 64