Counting principle

Question

Hale Middle School is going to select a committee. The committee will have a faculty member, a male student, a female student, a parent, and a school board member.

Here are the positions and the people interested in each.

POSITION
Faculty member	Mrs. Evans, Dr. Smith, Ms. Ross
Male student	Josh, Bob, Joe
Female student	Lena, Maya, Rita
Parent	Ms. Rivera, Mr. Rodriguez, Mrs. Lewis, Dr. Gray, Mrs. Baker
School board member	Ms. Bryant, Mr. Kelly, Dr. Nguyen

Based on this list, how many ways are there to fill the five committee positions?

Answer 1

There are 3 ways to fill the Faculty Member position.

There are 3 ways to fill the Male Student position.

There are 3 ways to fill the Female Student position.

There are 5 ways to fill the Parent position.

There are 3 ways to fill the School Board Member position.

So the possible ways to fill the committee are 3•3•3•5•3 = 405

They would be like this:

(where Fa₁ represents Faculty Member #1, etc):

Fa₁, M₁, Fe₁, P₁, S₁

Fa₁, M₁, Fe₁, P₁, S₂

Fa₁, M₁, Fe₁, P₁, S₃

Fa₁, M₁, Fe₁, P₂, S₁

Fa₁, M₁, Fe₁, P₂, S₂

Fa₁, M₁, Fe₁, P₂, S₃

Fa₁, M₁, Fe₁, P₃, S₁

Fa₁, M₁, Fe₁, P₃, S₂

Fa₁, M₁, Fe₁, P₃, S₃

Fa₁, M₁, Fe₁, P₄, S₁

Fa₁, M₁, Fe₁, P₄, S₂

Fa₁, M₁, Fe₁, P₄, S₃

Fa₁, M₁, Fe₁, P₅, S₁

Fa₁, M₁, Fe₁, P₅, S₂

Fa₁, M₁, Fe₁, P₅, S₃

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Fa₃, M₃, Fe₃, P₅, S₃