Engineering School Winter Party: Solving Tricky Combinations Question

[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?

 

[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?

 

[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

 

[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.