Math Problem Statement

You visit an ice cream shop on a hot summer day. The shop offers 15 ice cream flavors, 3 types of cones, and 8 toppings.

Assuming you want one ice cream flavor, one cone, and one topping, how many possible combinations can you create?

Solution

To find the total number of possible combinations, we multiply the number of choices for each category:

  • Ice cream flavors: 15 choices
  • Cones: 3 choices
  • Toppings: 8 choices

So, the total number of combinations is:

15×3×8=36015 \times 3 \times 8 = 360

Thus, you can create 360 possible combinations of one ice cream flavor, one cone, and one topping.

Would you like more details or have any questions about this?


Here are five related questions:

  1. What if you wanted two scoops of different ice cream flavors instead of just one?
  2. How would the number of combinations change if the shop added 2 more types of cones?
  3. What if you decided to skip the topping? How many combinations would you have then?
  4. What if the shop allowed up to 3 different toppings on a single cone? How would that affect the combinations?
  5. How many combinations would be possible if you could choose any combination of 2 different toppings?

Tip: When calculating combinations, multiply the number of options for each independent choice!

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Math Problem Analysis

Mathematical Concepts

Combinatorics
Multiplication Principle

Formulas

Total combinations = Number of flavors × Number of cones × Number of toppings

Theorems

Fundamental Principle of Counting

Suitable Grade Level

Grades 6-8