tents hold 2,3,5,6, or 12 people. how many combinations are possible to sleep 18
if all tents are fully occupied and exactly one 12 person tent is being used?
Since 12 of them sleep in the 12-person tent, we only have to sleep the other 6
people in some fully occupied 2,3,5, and 6-person tents.
It's obvious we can't use a 5-person tent.
To sleep those 6 people that aren't sleeping in the 12-person tent,
We can sleep them:
1. all in 1 6-person tent,
2. in 2 3-person tents, or
3. in 3 2-person-tents.
Just those 3 ways.
Edwin