Final answer:
In how many ways can you order a three-scoop ice cream cone with all different flavors from fifteen available at an ice cream parlor, where order does not matter? There are 455 different ways to order the ice cream cone using combinations in mathematics.
Step-by-step explanation:
The question concerns the number of ways you can order a three-scoop ice cream cone with all different flavors, given a choice of fifteen flavors, assuming that the order of the flavors does not matter. This situation can be addressed using combinations in mathematics, specifically the concept of the combination formula which is used to calculate the number of ways of selecting items from a group, where order does not matter.
To calculate the combinations, we use the formula for combinations C(n, k) = n! / (k! * (n - k)!), where 'n' represents the total number of items, 'k' represents the number of items to choose, 'n!' is the factorial of n, 'k!' is the factorial of k, and (n - k)! is the factorial of the difference between n and k.
In this case, we want to choose 3 flavors out of 15, so we will calculate C(15, 3). Using the combination formula:
- C(15, 3) = 15! / (3! * (15 - 3)!)
- C(15, 3) = 15! / (3! * 12!)
- C(15, 3) = (15 × 14 × 13) / (3 × 2 × 1) = 455
Therefore, you can order a three-scoop ice cream cone in 455 different ways when the order does not matter.