https://file.aiquickdraw.com/mathbot/file/1725869297044yvuzu0dg.jpg

https://file.aiquickdraw.com/mathbot/file/17258692970448jxcr2fl.jpg

The images you have uploaded seem to depict a problem related to a coffee survey where customer preferences were analyzed. From the text visible in the images, I can help break down the key information and approach solving it:

### From the first image:
The survey provides the following information:
- **221 customers** like espresso.
- **127 customers** like cappuccino and chocolate-flavored coffee.
- **182 customers** like cappuccino.
- **136 customers** like espresso and chocolate-flavored coffee.
- **209 customers** like chocolate-flavored coffee.
- **78 customers** like all three types of coffee (espresso, cappuccino, chocolate-flavored).
- **116 customers** like espresso and cappuccino.
- **82 customers** like none of these types of coffee.

### From the second image:
You are asked to determine how many customers:
a. Like **only** chocolate-flavored coffee.
b. Like **cappuccino and chocolate-flavored** coffee but not espresso.
c. Like **espresso and cappuccino** but not chocolate-flavored coffee.
d. Like **exactly one** of the three types of coffee.

### Plan for solution:
We can approach this as a **Venn Diagram** problem where we have three sets:
1. **Espresso** (E)
2. **Cappuccino** (C)
3. **Chocolate-flavored coffee** (Ch)

The goal is to fill out all regions of the Venn Diagram based on the given data. Once we have all regions identified, we can answer the specific questions.

Would you like me to continue by filling out the Venn Diagram and solving these sub-questions?

How many customers like only chocolate-flavored coffee, like cappuccino and chocolate-flavored coffee but not espresso, like espresso and cappuccino but not chocolate-flavored coffee, and like exactly one of the three types of coffee?

Analyze customer preferences in a coffee survey using set theory and Venn diagrams. Determine how many customers like only chocolate-flavored coffee, combinations of cappuccino, espresso, and more. A real-world example of applying the Inclusion-Exclusion Principle.

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