Lol, I am in an introductory section to the Addition and Multiplication Prinicples for counting sets/number of outcomes/possibilities.

I am still having a hard time wrapping my head around how this all works

Information:

6 students; Matthew, Mark, Luke, John, Paul, and James.

The officer positions; chairperson, secretary, and treasurer.

Question:

How many selections are there in which either Matt is chairperson or he is not an officer?

What I came up with is this,

As a chairperson -> there are 5 ways to choose 2nd position, 4 ways to choose 3rd position. Total 5 * 4 = 20 outcomes

non-officer -> there are 5 ways to choose 1st position, 4 for 2nd position, & 3 for 3rd position Total 5 * 4 * 3 = 60 outcomes

Using the Adding Principle 20 + 60 = 80 possible outcomes with matt and a chairperson or as a non-officer.

Am I even close? Thanks