Counting Principles

Probability · Axiom Academy

Fundamental techniques for counting outcomes in probability problems 1. The Multiplication Principle If a procedure consists of multiple sequential steps, and each step can be performed independently, multiply the number of options at each step. Example: Creating an outfit with 3 shirts and 4 pants: 2. Multiplication Principle: PIN Example Let's apply the multiplication principle to a real-world example: creating a 4-digit PIN. Watch how the possibilities multiply: If you can complete a task by choosing from several mutually exclusive methods, add the number of ways for each method. Example: Traveling from City A to City B by car (3 routes) OR by train (2 routes): The key is identifying whether the choices are sequential (multiply) or alternative (add). Let's compare both principles side by side:

This is the written version of the interactive lesson above. See the full Probability course.