Let's break down how to solve this problem and choose the correct counting technique.

Part 1: How many different sundaes can you create using one ice cream flavor and one topping?

We are selecting one ice cream flavor from a group of 27 different flavors and one topping from a group of 6 different toppings. This situation fits the multiplication principle because we are combining choices from two independent sets (flavors and toppings).

• For each of the 27 ice cream flavors, you can choose one of 6 toppings.
• The total number of possible sundaes is simply the product of these two numbers, which is: $27 \times 6 = 162$ Thus, you can create 162 different sundaes.

Why we use the Multiplication Principle:

• Explanation: We use the multiplication principle when we are selecting one item from each of two (or more) independent sets, and every combination of choices is valid. Here, since you are choosing one flavor and one topping, and these choices are independent (your choice of flavor doesn’t affect your choice of topping), the total number of combinations is the product of the two sets' sizes.

Hence, the correct choice is B. The multiplication principle.

Final Answer:

You can create 162 different sundaes.

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Would you like more details on the next part of the problem or any clarifications?

Here are 5 related questions that could deepen your understanding:

1. What if the shop allowed two different toppings instead of one?
2. How would the total number of sundaes change if the shop offered 3 toppings instead of 6?
3. Can you calculate how many sundaes could be made with two scoops, where the second scoop can be any flavor?
4. How many sundae combinations could you create if you could choose up to 3 toppings?
5. What would the total number of combinations be if some toppings were not available with certain flavors?

Tip: When applying the multiplication principle, always verify that the choices are independent, meaning one choice does not restrict or affect another.