Least You Need to Know: Inclusion-Exclusion
Open lesson
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
Open lesson
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
Open lesson
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
Open lesson
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
Open lesson
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
Open lesson
Stars and bars counts ways to distribute identical objects into distinct boxes by turning the problem into positions for separators.