The problem involves selecting three scoops of ice cream from seven different flavors, where the order of the scoops matters because each position (top, middle, bottom) is distinct. This is a permutation problem because each flavor is unique, and the order is important.

Solution:

• There are 7 choices for the flavor of the top scoop.
• After choosing the top scoop, there are 6 remaining choices for the middle scoop.
• After choosing the middle scoop, there are 5 remaining choices for the bottom scoop.

Thus, the total number of ways to choose a cone is: $7 \times 6 \times 5 = 210$

So, the number of ways to choose the cone if order matters is 210.

Would you like more details on this explanation or have any questions?

Here are five related questions for further practice:

1. How many ways can you choose a cone if the order does not matter?
2. What if you can have multiple scoops of the same flavor? How many combinations are possible?
3. If there were only 5 flavors, how many ways could you choose 3 scoops if order matters?
4. How many ways can you choose 4 scoops from 7 flavors if no flavor is repeated and the order matters?
5. What is the difference between permutation and combination in problems like this?

Tip:

When dealing with selection problems, always determine if the order of selection matters. If it does, you're dealing with permutations; if not, it's a combination problem.