Answer:
1820 different ways
Explanation:
To calculate the number of ways you can choose 4 different snacks out of 16 available snacks, we can use the concept of combinations.
The number of ways to choose r items out of n items, without considering the order, is given by the binomial coefficient formula:
C(n, r) = n! / (r! * (n - r)!)
where n! denotes the factorial of n.
In this case, we have 16 snacks to choose from (n = 16), and we want to choose 4 different snacks (r = 4). Using the formula, we can calculate the number of ways:
C(16, 4) = 16! / (4! * (16 - 4)!)
C(16, 4) = 16! / (4! * 12!)
C(16, 4) = (16 * 15 * 14 * 13) / (4 * 3 * 2 * 1)
C(16, 4) = 43680 / 24
C(16, 4) = 1820
Therefore, there are 1820 different ways you can choose 4 snacks out of the 16 available snacks at the hockey arena snack bar.