Question

a) Suppose that a popular style of running shoe is available for both men and women. The woman's shoe comes in sizes $6,7,8$, and 9 , and the man's shoe comes in sizes $8,9,10,11$, and 12 . The man's shoe comes in white and black, while the woman's shoe comes in white, red, and black. Use a tree diagram to determine the number of different shoes that a store has to stock to have at least one pair of this type of running shoe for all available sizes and colors for both men and women. b) Answer the question in part (a) using counting rules.

Name: Problem 57, Chapter 5: Discrete Mathematics and Its Applications
Uploaded: 2023-05-02T18:12:07-08:00
Duration: 2 min 57 s
Channel: Clayton Schubring

   a) Suppose that a popular style of running shoe is available for both men and women. The woman's shoe comes in sizes $6,7,8$, and 9 , and the man's shoe comes in sizes $8,9,10,11$, and 12 . The man's shoe comes in white and black, while the woman's shoe comes in white, red, and black. Use a tree diagram to determine the number of different shoes that a store has to stock to have at least one pair of this type of running shoe for all available sizes and colors for both men and women.
b) Answer the question in part (a) using counting rules.

Discrete Mathematics and Its Applications

Kenneth H. Rosen 6th Edition

Chapter 5, Problem 57

Instant Answer

Solved by Expert Clayton Schubring

05/02/2023

Step 1

### Part (a): Using a Tree Diagram ** Show more…

Show all steps

Thanks for your feedback!

a) Suppose that a popular style of running shoe is available for both men and women. The woman's shoe comes in sizes $6,7,8$, and 9 , and the man's shoe comes in sizes $8,9,10,11$, and 12 . The man's shoe comes in white and black, while the woman's shoe comes in white, red, and black. Use a tree diagram to determine the number of different shoes that a store has to stock to have at least one pair of this type of running shoe for all available sizes and colors for both men and women. b) Answer the question in part (a) using counting rules.

Play audio

Feedback

Clayton Schubring and 99 other educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Tree Diagrams

A tree diagram is a visual tool used to systematically illustrate all possible outcomes of a sequence of events or decisions. It helps in breaking down complex problems by mapping each choice or step as a branch, ensuring that every possible combination is accounted for without repetition or omission.

Fundamental Counting Principle

The Fundamental Counting Principle, also known as the multiplication rule, is a method used to determine the total number of possible outcomes in a multi-step process by multiplying the number of choices available at each independent step. This principle is crucial in scenarios involving several categories or criteria, as it simplifies the process of calculating combinations or permutations.

Please give Ace some feedback