We have a total set of 15 people, we need to arrange them in 4 spots, where each individual must be unique. Therefore we have:
[tex]\text{ Combinations}=15\cdot14\cdot13\cdot12=32760[/tex]
There are 32760 possible solutions.
We then need to choose 12 appetizers from a set of 16 appetizers, where each individual appetizer must be unique, so we have:
[tex]\text{Combinations}=\frac{16!}{(16-12)!}=\frac{16!}{4!}=871782912000[/tex]
There are 871782912000 possible solutions.
