Enumerative Combinatorics · Counting principles, bijections, and the pigeonhole principle
A group has six distinct volunteers
Problem
A group has six distinct volunteers. An organizer will either: - assign three different volunteers to the distinct roles of opener, demonstrator, and closer; or - choose a three-person team with no roles. How many outcomes are possible in each case? Explain exactly why division by \(3!\) is valid for the team count and invalid for the role assignment count.
Hint
Decide what information distinguishes one outcome from another in each experiment.
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