Question

A yogurt shop offers 6 different flavors of frozen yogurt and 12 different toppings. How many choices are possible?(1 point) Responses 72 72 144 144 36 36 665,280

Answer 1

To find the total number of choices available at the yogurt shop, we need to consider that you can choose one of the 6 flavors of frozen yogurt and combine it with any of the 12 toppings. For each flavor, you can choose to add any combination of toppings.

Here's how to calculate the total number of combinations:

1. **Choosing a Flavor**: There are 6 choices for the frozen yogurt flavor.
2. **Choosing Toppings**: For the toppings, each of the 12 toppings can either be included or not included in your yogurt, giving you 2 options per topping (include or don't include). Thus, for 12 toppings, you have \(2^{12}\) combinations of toppings.

Now, let's calculate \(2^{12}\):

\[
2^{12} = 4096
\]

So, the total number of choices for toppings is 4096.

Next, we multiply the number of flavor choices by the number of topping combinations:

\[
6 \text{ (flavors)} \times 4096 \text{ (topping combinations)} = 24576
\]

So, the total number of choices possible at the yogurt shop is **24,576**. None of the options you provided seem correct based on the calculations.

If you are looking for a specific answer among the choices, check to ensure you're accounting for combinations correctly or clarify the question.