Permutations, Combinations, and Tree Diagrams

Draw a tree diagram showing how many different outfits you can make with a gray shirt, a pink shirt, and a black shirt; and crocs, sandals, or tennis-shoes. How many different outcomes can you have?

• 6

• 9

• 27

• 12

Based off of your tree diagram, what is the probability that you choose a pink shirt and crocs?

• 1/9

• 1/6

• 1/12

• 1/27

Kelly is buying a cake. She has a choice of either chocolate or vanilla cake; chocolate frosting, cream cheese frosting, or buttercream frosting; and strawberries, Oreos, or sprinkles as a topper. Draw a tree diagram to represent this. How many different options does she have?

• 8

• 9

• 18

• 12

How many of those options include chocolate frosting?

• 1/3

• 1/9

• 1/18

• 1/2

What is the probability that she gets a vanilla cake?

• 1/9

• 1/6

• 1/2

• 1/3

Students running a race would be a .....

• Combination

• Permutation

7 students want to finish 1st, 2nd, or 3rd for a race - how many different outcomes are possible?

• 21

• 35

• 210

• 3

The class of 2026 is electing 3 class representatives. (All of the same status and power level)

• Permutation

• Combination

146 students elect 3 representatives. How many different outcomes are possible?

• 3048480

• 508080

• 438

• 3

146 students elect a president, vice president, and treasurer - how many outcomes are possible?

• 3048480

• 508080

• 438

• 3