Engineering School Winter Party: Solving Tricky Combinations Question

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Homework Help Overview

The problem involves determining the number of different sets of attendees for a Winter Solstice party hosted by the dean of an Engineering School, where 9 department chairpersons and their spouses are invited. The conditions specify that department chairs can attend without their spouses, but spouses cannot attend without their respective chairs.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants suggest starting with simpler cases, such as one or two department chairs, to build understanding of the problem's structure. Others focus on the representation of a single chair at the event and the implications of spouse attendance.

Discussion Status

The discussion is ongoing, with participants exploring different approaches to the problem. Some guidance has been offered regarding simplifying the problem by considering fewer department chairs, but no consensus has been reached on a complete solution.

Contextual Notes

Participants note that the complexity of the problem increases with the number of department chairs, and the specific conditions regarding spouse attendance are central to the discussion.

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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?
 
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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?
 
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
 
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.
 

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