Least You Need to Know: Inclusion-Exclusion
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When two counted groups overlap, add the group sizes and then subtract the overlap once.
Counting Principles
Multiply, add, and avoid overcounting in basic counting problems.
6 lessons · 38 questions
Counting Principles
Multiply, add, and avoid overcounting in basic counting problems.
6 lessons · 38 questions
Inclusion Exclusion
1 lessons · 7 questions
Permutations And Combinations
1 lessons · 8 questions
Least You Need to Know: Permutations and Combinations
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Use a **permutation** when order matters. Use a **combination** when order does not matter.
Pigeonhole Principle
1 lessons · 3 questions
Least You Need to Know: The Pigeonhole Principle
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If you place more objects than boxes into the boxes, at least one box must contain more than one object. Use the ceiling idea for stronger versions.
Product And Sum Rules
1 lessons · 8 questions
Least You Need to Know: Product Rule and Sum Rule
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Many counting errors come from not noticing whether choices happen **in sequence** or belong to **separate non-overlapping cases**.
Restricted Arrangements
1 lessons · 8 questions
Least You Need to Know: Restricted Arrangements
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Harder counting problems often become easier once you decide whether order matters, whether items repeat, and whether a restriction should be handled first or by subtraction.
Stars And Bars
1 lessons · 4 questions
Least You Need to Know: Stars and Bars
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Stars and bars counts ways to distribute identical objects into distinct boxes by turning the problem into positions for separators.