Quoting part of my homework/assignment:
How many keys are required for secure communication among 1000 person if:
- Symmetric key encryption algorithm is used?
- Asymmetric key encryption algorithm is used?
For symmetric they each need to maintain and transfer their own key, so probably $1000 \times 1000$, and for asymmetric maybe just $2000$, each having one public one private.
Is that correct?