At the beginning of 2002, an ice cream shop claimed to have "nearly 944 different ice cream flavors." Assuming that you could choose from 944 different flavors, that you could have your ice cream in a cone, a cup, or a sundae, and that you could choose from a dozen different toppings, how many different desserts could you have?

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desserts

To find the total number of different desserts you could have, we need to consider all the possible combinations of flavors, types of containers, and toppings.

### Breakdown of the problem:

1. **Ice cream flavors**: There are 944 different flavors.
2. **Containers**: You can choose from 3 different options (cone, cup, or sundae).
3. **Toppings**: You can choose from 12 different toppings, and toppings can either be included or excluded (since you can have no toppings, some, or all of them).

Each topping is an independent choice (either you add it or you don't), so the number of combinations of toppings is \(2^{12}\) because for each topping, there are 2 possibilities: include it or don't include it.

### Calculation:

- Number of choices for **flavors**: 944
- Number of choices for **containers**: 3
- Number of choices for **toppings**: \(2^{12}\)

So the total number of different desserts is:
\[
\text{Total desserts} = 944 \times 3 \times 2^{12}
\]
\[
\text{Total desserts} = 944 \times 3 \times 4096
\]
\[
\text{Total desserts} = 11,601,792
\]

Thus, the total number of different desserts you could have is **11,601,792**.

### Would you like more details or have any questions?

Here are some related questions you might find interesting:

1. What if there were only 5 toppings instead of 12? How many different desserts could you have?
2. How does the number of different desserts change if you could only choose up to 3 toppings?
3. What if you had to choose exactly one topping for each dessert? How many different options would you have then?
4. How many different desserts could you have if one topping option could only be chosen once per container type?
5. What would happen if you could choose multiple flavors for a single dessert?

**Tip**: When dealing with combinations, consider how many independent choices you're making for each variable involved in the problem!

At the beginning of 2002, an ice cream shop claimed to have 'nearly 944 different ice cream flavors.' Assuming that you could choose from 944 different flavors, that you could have your ice cream in a cone, a cup, or a sundae, and that you could choose from a dozen different toppings, how many different desserts could you have?

Find out how to calculate the total number of different desserts you could make with 944 ice cream flavors, 3 container types (cone, cup, sundae), and 12 toppings. This problem uses combinatorics and the multiplication principle to show you all the possible combinations. Suitable for high school students.

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