Multiplication Principle

The Multiplication Principle says that if one task can be done in \( m \) ways and a second task in \( n \) ways, then both tasks together can be done in \( m \times n \) ways.

We use the Multiplication Principle when tasks are performed in sequence.

Examples:

• If you have 4 shirts and 3 pairs of pants, you have \( 4 \times 3 = 12 \) different outfits.
• A password has 2 letters (26 options each) followed by 2 digits (10 options each), so there are \( 26^2 \times 10^2 \) total passwords.

The principle assumes that each task is independent of the others.

We often apply the Multiplication Principle to problems involving ordered selections.