We will see that Eric can choose out of 105 different groups of 13 elements.
How many groups of 13 appetizers are possible?
Suppose that we have a set of N elements, the number of different sets of K elements (K ≤ N) that we can make out of the N elements is:
[tex]C(N, K)= \frac{N!}{(N - K)!*K!}[/tex]
In this particular case, we have N = 15 and K = 13, replacing that we get:
[tex]C(15, 13) = \frac{15!}{(15 - 13)!*13!} = \frac{15*14}{2} = 15*7 = 105[/tex]
This means that are 105 different groups of 13 appetizers that Eric can choose.
If you want to learn more about combinations:
https://brainly.com/question/11732255
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