Final answer:
To calculate different arrangements, we use combinations. For Finn's stuffed animals, we would calculate the combinations separately for choosing 1, 2, or 3 out of 12 animals and add them together. The total possible arrangements would be 298, which suggests a discrepancy with the provided answer choices.
Step-by-step explanation:
Finn is arranging his favourite stuffed animals on a shelf, choosing up to 3 out of his 12 different stuffed animals, and we want to determine the number of different arrangements he could select. This is a classic combinatorics problem, requiring the calculation of combinations when order does not matter.
To solve this, we can use the combinations formula, which is 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 '!' stands for factorial, meaning the product of all positive integers up to that number.
For choosing up to 3 animals, we have to consider selecting 1, 2, and 3 animals separately and sum those possibilities:
- Choosing 1 out of 12 gives us C(12, 1) = 12 combinations.
- Choosing 2 out of 12 gives us C(12, 2) = 12! / (2! * 10!) = 66 combinations.
- Choosing 3 out of 12 gives us C(12, 3) = 12! / (3! * 9!) = 220 combinations.
Adding these up gives us a total of 12 + 66 + 220 = 298 arrangements possible, which is not one of the options provided, so there might be a misunderstanding with the question or a typo in the options.