Counting Principles: Apply It

  • Solve counting problems using the Addition and Multiplication Principles.
  • Solve counting problems using permutations and combinations.
  • Solve counting problems using permutations involving n non-distinct objects.

Music Festival Planning

A regional music festival is in the final stages of planning their three-day event. The organizing team needs to make a series of decisions — from scheduling performers to designing merchandise bundles — and counting principles will help them understand exactly how many options they’re working with.

Scheduling the Opening Night Lineup

The festival has confirmed 8 performers for opening night. The production team needs to finalize the performance order for the first 3 slots of the evening, as these spots receive the most promotion and media coverage. The order matters — the opening act, the second act, and the headline opener are each featured differently in marketing materials.

How many ways can the production team arrange 3 performers in the first 3 slots from their 8 confirmed acts?

Selecting the Volunteer Leadership Team

The festival relies on a pool of 150 trained volunteers. For the event weekend, the organizing committee needs to select 5 volunteers to serve as team leaders. All 5 leaders have the same responsibilities and title.

How many ways can the committee select 5 team leaders from 150 volunteers?