### Title: Dance Competition Survey Results#### IntroductionA survey was conducted at a local ballroom dance studio asking students which dances they competed in at the most recent competition. Below are the results for the dances Mambo, Swing, and Paso Doble.#### Venn Diagram ExplanationA Venn diagram is used to display the data, showing the number of students participating in each dance and their combinations:- **Mambo Only**: 297 students- **Swing Only**: 278 students- **Paso Doble Only**: 319 students- **Mambo & Swing**: 293 students- **Swing & Paso Doble**: 277 students- **Mambo & Paso Doble**: 216 students- **All Three Dances (Mambo, Swing, Paso Doble)**: 386 students- **Paso Doble Only**: 393 students who only participated in Paso Doble without overlapping with the other two categories.#### Questionsa) **How many students competed in none of these three dances?**b) **How many students competed in both Mambo & Swing, or competed in both Swing & Paso Doble?**c) **How many students competed in Mambo or Paso Doble, but not Swing?**### ConclusionThis data helps in understanding participation trends and preferences among the students at the dance studio. Use these insights to plan future events or gauge interest in specific dance styles. The image contains a Venn diagram and a series of questions related to a student dance competition involving Mambo, Swing, and Paso Doble.**Venn Diagram:**- Three overlapping circles represent participation in Mambo, Swing, and Paso Doble.- The circle for Paso Doble has the numbers as follows: 393 students (in blue), 319 students (in purple). **Questions:**a) How many students competed in none of these three dances?b) How many students competed in Mambo & Swing or competed in Swing & Paso Doble?c) How many students competed in Mambo or Paso Doble, but not Swing?d) How many students competed in Swing & Paso Doble, but not Mambo?e) How many students competed in Mambo, Swing, or Paso Doble?These questions require analysis of the Venn diagram to solve for the number of students that meet each specified category.

Name: ### Title: Dance Competition Survey Results#### IntroductionA survey
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Description: ### Title: Dance Competition Survey Results#### IntroductionA survey was conducted at a local ballroom dance studio asking students which dances they competed in at the most recent competition. Below are the results for the dances Mambo, Swing, and

Answered: Image /qna-images/answer/c31045a0-26ce-45f9-8890-31dee0f4ce09.jpg

Answered: Swing Mambo 293 297 278 386 216 277 393…

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Swing Mambo 293 297 278 386 216 277 393 319 Paso Doble a) How many students competed in none of these three dances? b) How many students competed in Mambo & Swing or competed in Swing & Pa

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Permutations and Combinations

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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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### Title: Dance Competition Survey Results

#### Introduction
A survey was conducted at a local ballroom dance studio asking students which dances they competed in at the most recent competition. Below are the results for the dances Mambo, Swing, and Paso Doble.

#### Venn Diagram Explanation
A Venn diagram is used to display the data, showing the number of students participating in each dance and their combinations:

- **Mambo Only**: 297 students
- **Swing Only**: 278 students
- **Paso Doble Only**: 319 students

- **Mambo & Swing**: 293 students
- **Swing & Paso Doble**: 277 students
- **Mambo & Paso Doble**: 216 students

- **All Three Dances (Mambo, Swing, Paso Doble)**: 386 students

- **Paso Doble Only**: 393 students who only participated in Paso Doble without overlapping with the other two categories.

#### Questions

a) **How many students competed in none of these three dances?**

b) **How many students competed in both Mambo & Swing, or competed in both Swing & Paso Doble?**

c) **How many students competed in Mambo or Paso Doble, but not Swing?**

### Conclusion
This data helps in understanding participation trends and preferences among the students at the dance studio. Use these insights to plan future events or gauge interest in specific dance styles.

The image contains a Venn diagram and a series of questions related to a student dance competition involving Mambo, Swing, and Paso Doble.

**Venn Diagram:**
- Three overlapping circles represent participation in Mambo, Swing, and Paso Doble.
- The circle for Paso Doble has the numbers as follows: 393 students (in blue), 319 students (in purple).

**Questions:**

a) How many students competed in none of these three dances?

b) How many students competed in Mambo & Swing or competed in Swing & Paso Doble?

c) How many students competed in Mambo or Paso Doble, but not Swing?

d) How many students competed in Swing & Paso Doble, but not Mambo?

e) How many students competed in Mambo, Swing, or Paso Doble?

These questions require analysis of the Venn diagram to solve for the number of students that meet each specified category.

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