I'm new to Combinatorics and would like to understand the idea of the following combinatorics questions:

In How many ways can you sit 4 couples on a bench such that:

1. Lucy always sits to the left of Carol (Not necessarily adjacent).

I was trying to count all the options for sitting Lucy (first place, second place and so on) but I'm sure there's more elegant way of doing that. Just to be sure the result I got is: 30,960 ways.

2. Lucy would never sit next to its partner and Carol would never sit next to its partner.