# Tricky Combinations Question

1. Sep 7, 2011

### dspampi

The dean of an Engineering School invites all 9 department chairpersons and their spouses to his house for a Winter Solstice party. If each department chair may attend without a spouse, but the spouse may not attend without the department chair, how many different sets of attendees are possible?

Anyone know the logic to set this answer up?

2. Sep 7, 2011

### Dick

Try it for the case of 1 department chair. Now do 2. You can count those pretty easily. Now do you see how to get to 9?

3. Sep 7, 2011

### phinds

Forget about the fact that there are 9 of them, for the moment, and just focus on one chair. How many ways can the chair be represented at the event?

EDIT: I see Dick beat me to it

4. Sep 7, 2011

### daveb

Actually, for a precaclulus math class, that can be a pretty complex problem, since for each possible set of department chairs that can show up, their corresponding spouses may or may not necessarily show up as well.