Fundamental Counting Principle – The Multiplication Rule

The tables and trees from the last two pages both led to the same pattern: multiply the number of choices at each stage together. That pattern has a name – the Fundamental Counting Principle: if one event can happen in m ways, and a second, independent event can happen in n ways, then both events together can happen in m × n ways. With three or more independent events, simply keep multiplying.

This principle is the single most important idea in this entire section – permutations, combinations, and every other formula you'll meet are really just the Fundamental Counting Principle applied to specific, common situations.

Applying the Fundamental Counting Principle

Real-Life Application

• Licence plates: the total number of possible plates is found using this principle.
• Product customisation: the number of possible product configurations (colour, size, material) multiplies out this way.
• Genetics: the number of possible gene combinations from two parents follows this same multiplication rule.

Key Takeaways

Practice: Fundamental Counting Principle