2. A small boutique clothing store does not have a lot of products; however, the quality of clothing is superior to their department store counterpart. The boutique clothing store has five different colored pants: blue, brown, black, gray, and khaki; six different colored shirts: pink, yellow, red, blue, violet, and green; and three different types of shoes: loafer, oxford, and boot. Part A: How many combinations of clothing and shoes are available? Part B: What is the probability that a customer buys khaki pants?
2. A small boutique clothing store does not have a lot of products; however, the quality of clothing is superior to their department store counterpart. The boutique clothing store has five different colored pants: blue, brown, black, gray, and khaki; six different colored shirts: pink, yellow, red, blue, violet, and green; and three different types of shoes: loafer, oxford, and boot. Part A: How many combinations of clothing and shoes are available? Part B: What is the probability that a customer buys khaki pants?
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Concept explainers
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
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Question
![**Combinatorics and Probability in Fashion Retail**
---
In this exercise, you will explore basic principles of combinatorics and probability using an example from a small boutique clothing store.
---
### Scenario Analysis:
A small boutique clothing store does not have a lot of products; however, the quality of its clothing is superior to that of their department store counterpart. The boutique clothing store offers:
- **Five different colored pants**: blue, brown, black, gray, and khaki.
- **Six different colored shirts**: pink, yellow, red, blue, violet, and green.
- **Three different types of shoes**: loafer, oxford, and boot.
---
### Problem Statement:
#### Part A:
How many combinations of clothing and shoes are available?
To find the total number of combinations for different outfits including pants, shirts, and shoes, you multiply the number of options for each category:
- Pants options: 5
- Shirts options: 6
- Shoes options: 3
Formula: Number of combinations = Pants options × Shirts options × Shoes options
Let's calculate:
\[ 5 \text{ pants} \times 6 \text{ shirts} \times 3 \text{ shoes} = 90 \text{ combinations} \]
Hence, there are 90 different combinations of clothing and shoes available at the boutique.
---
#### Part B:
What is the probability that a customer buys khaki pants?
The probability of an event is the ratio of the favorable outcomes to the total possible outcomes. Here, the customer buying khaki pants is the event of interest:
- Probability (buying khaki pants) = Number of favorable outcomes / Total possible outcomes
There are 5 colors of pants, and khaki is one of them:
\[ \text{Probability} = \frac{1}{5} = 0.20 \]
So, the probability that a customer buys khaki pants is 0.20 or 20%.
---
By understanding these basic principles of combinatorics and probability, you can better appreciate how different choices can combine to create a variety of options, a useful skill in both fashion retail and many other fields.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe5ed07d5-7a8f-4097-9c81-82df457ca627%2F408d9f82-3a0b-48b2-bb7c-8fd5f28e40fa%2Fwm0zy4p_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Combinatorics and Probability in Fashion Retail**
---
In this exercise, you will explore basic principles of combinatorics and probability using an example from a small boutique clothing store.
---
### Scenario Analysis:
A small boutique clothing store does not have a lot of products; however, the quality of its clothing is superior to that of their department store counterpart. The boutique clothing store offers:
- **Five different colored pants**: blue, brown, black, gray, and khaki.
- **Six different colored shirts**: pink, yellow, red, blue, violet, and green.
- **Three different types of shoes**: loafer, oxford, and boot.
---
### Problem Statement:
#### Part A:
How many combinations of clothing and shoes are available?
To find the total number of combinations for different outfits including pants, shirts, and shoes, you multiply the number of options for each category:
- Pants options: 5
- Shirts options: 6
- Shoes options: 3
Formula: Number of combinations = Pants options × Shirts options × Shoes options
Let's calculate:
\[ 5 \text{ pants} \times 6 \text{ shirts} \times 3 \text{ shoes} = 90 \text{ combinations} \]
Hence, there are 90 different combinations of clothing and shoes available at the boutique.
---
#### Part B:
What is the probability that a customer buys khaki pants?
The probability of an event is the ratio of the favorable outcomes to the total possible outcomes. Here, the customer buying khaki pants is the event of interest:
- Probability (buying khaki pants) = Number of favorable outcomes / Total possible outcomes
There are 5 colors of pants, and khaki is one of them:
\[ \text{Probability} = \frac{1}{5} = 0.20 \]
So, the probability that a customer buys khaki pants is 0.20 or 20%.
---
By understanding these basic principles of combinatorics and probability, you can better appreciate how different choices can combine to create a variety of options, a useful skill in both fashion retail and many other fields.
Transcribed Image Text:### Probability Questions for Educational Purposes
**Part C:**
What is the probability that a customer buys a pair of boots with blue pants?
**Part D:**
What is the probability that a customer buys brown pants, a yellow shirt, and an oxford shoe?
**Part E:**
What is the probability that a customer buys brown pants, a yellow shirt, OR an oxford shoe?
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