The Subtraction Principle

Combinatorics · Axiom Academy

LESSON The Subtraction Principle Total outcomes in the universal set U Unwanted outcomes in the complement A' 2 When to Use the Subtraction Principle "At least one" - Easier to count "none" and subtract "Not all the same" - Count "all the same" and subtract "Contains X" - Count "doesn't contain X" and subtract Complex inclusion - Simple exclusion criterion 4 Example: Not All the Same Color Ask: Which is simpler to count - what I want or what I don't want? Look for: Words like "at least," "not all," "contains," "some" Consider: Can the complement be counted in one or two steps? Calculate both: If unsure, estimate difficulty of both approaches Remember: The easier path is always the right one!

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