Given a number of people (represented by the letter $p$), and a number of chairs (represented by the letter $c$), what equation can I use to figure out how many possible seating arrangements there are?
Chairs can be empty and not everyone has to be in a chair.
So for example given 3 chairs and 5 people the following 6 options exist for the first chair:
- chair is empty
- person A sits in chair
- person B sits in chair
- person C sits in chair
- person D sits in chair
- person E sits in chair
For the second chair it gets really complicated. If no one sits in the first chair then you have the same 6 options available for the second chair, however if, for example, person B sits in the first chair, you have 5 options (the six above not including "person B sits in chair") available for the second chair. It gets really complicated from here.
BTW, I'm kind of new to the subject and I'm not sure what tags to use. I'd appreciate it if someone could add the relevant tags.