https://file.aiquickdraw.com/mathbot/file/1727409187829y0ruwc0i.jpg

To determine how many different sets of classes Jessica can take, let's break it down:

1. **Available Choices**:
   - Economics: 3 choices
   - Mathematics: 2 choices
   - Education: 5 choices, but the 2 most popular classes are full, so only \( 5 - 2 = 3 \) choices are available.
   - Sociology: 3 choices

2. **Number of Different Sets**:
   Since she must take exactly one class from each category, the total number of combinations is the product of available choices from each category.

   The total number of different sets of classes is:
   \[
   3 \times 2 \times 3 \times 3 = 54
   \]

Thus, **Jessica has 54 different sets of classes to choose from**.

Would you like further details or have any other questions?

Here are 5 related questions to think about:
1. What if one more class in Education becomes unavailable? How does it affect the total sets of classes?
2. How many sets of classes could Jessica take if only 1 class was unavailable in Education?
3. What would happen if there were an additional category, such as History, with 4 class options?
4. How would the problem change if some Mathematics classes became full?
5. What if Jessica could take 2 classes from any category instead of one?

**Tip**: When dealing with combinations, always remember that the total number of possibilities is a product of available options.

Jessica's class schedule for next semester must consist of exactly one class from each of the four categories: Economics (3 choices), Mathematics (2 choices), Education (5 choices but 2 most popular are full), and Sociology (3 choices). Determine the number of different sets of classes Jessica can take.

Find out how many different sets of classes Jessica can choose for her schedule. She has 3 choices in Economics, 2 in Mathematics, 3 in Education (after accounting for 2 unavailable classes), and 3 in Sociology. This combinatorics problem uses the multiplication principle and is suitable for students in Grades 9-11.

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