Question

Hello can you please explain step by step how to work this out. It’s my first time doing it.

Answer 1

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:

$\text{ Combinations}=15\cdot14\cdot13\cdot12=32760$

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:

$\text{Combinations}=\frac{16!}{(16-12)!}=\frac{16!}{4!}=871782912000$

There are 871782912000 possible solutions.