Final answer:
To determine the number of possible outcomes for Kevin selecting 3 out of 12 orange juice brands, the combination formula C(n, k) = n! / (k!(n-k)!) is used, resulting in 220 possible outcomes.
Step-by-step explanation:
The student's question, "Kevin is selecting 3 out of 12 possible different brands of orange juice at the store. How many possible outcomes exist?", deals with the concept of combinations in mathematics. To determine the number of possible outcomes we can use the combinations formula, which is given by:
C(n, k) = n! / (k!(n-k)!), where n is the total number of items to choose from, k is the number of items to choose, and ! denotes factorial.
Since Kevin is selecting 3 different brands out of 12 available, we plug these numbers into the formula:
C(12, 3) = 12! / (3!(12-3)!) = 12! / (3!9!)
The factorial of a number is the product of all positive integers less than or equal to that number. For example, 4! = 4×3×2×1. Thus, we can simplify the numbers as follows:
C(12, 3) = (12×11×10) / (3×2×1) = 220
Therefore, there are 220 possible outcomes when Kevin selects 3 out of 12 brands of orange juice.