Final answer:
There are 816 different ways to get a Snow Storm with three different mix-ins at Dairy Princess, calculated using the combination formula C(18, 3).
Step-by-step explanation:
The subject of the question is Combinatorics, a branch of mathematics concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. The question can be solved using the concept of combinations in mathematics, which refers to finding the number of ways to select items from a group, where order does not matter.
Since there are 18 different possible mix-ins available at Dairy Princess and the student can choose three different mix-ins for their Snow Storm, we must determine the number of combinations of 18 items taken 3 at a time (denoted as 18 choose 3). This can be calculated using the combination formula, which is:
C(n, k) = n! / (k!(n-k)!)
Where n represents the total number of items to choose from (18 mix-ins), k represents the number of items to choose (3 mix-ins), and n! represents the factorial of number n, which is the product of all positive integers up to n.
Using the combination formula, we calculate 18 choose 3 as follows:
- Calculate the factorial of 18 (18!): 18 × 17 × 16 × ... × 1.
- Calculate the factorial of 3 (3!): 3 × 2 × 1.
- Calculate the factorial of (18-3) which is 15 (15!): 15 × 14 × ... × 1.
- Substitute these values into the combination formula: C(18, 3) = 18! / (3! × (18-3)!).
- Simplify the factorials by canceling out the common terms (15! in both numerator and denominator).
- Conclude with the result: 18 × 17 × 16 / (3 × 2 × 1) = 816
Therefore, there are 816 different ways to get a Snow Storm with three different mix-ins at Dairy Princess.