Counting cheat sheet
Counting cheat sheet
Section titled “Counting cheat sheet”Sum rule
Section titled “Sum rule”If you are choosing one outcome from disjoint cases, add the counts.
Formula: a + b + c
Signal words: either, one of, separate cases.
Product rule
Section titled “Product rule”If a task is done in stages, multiply the number of choices per stage.
Formula: a × b × c
Signal words: first, then, for each.
Permutations
Section titled “Permutations”Use when you arrange distinct items and order matters.
Formula: P(n, r) = n! / (n-r)!
Signal words: line up, arrange, rank, seat.
Combinations
Section titled “Combinations”Use when you choose items and order does not matter.
Formula: C(n, r) = n! / (r!(n-r)!)
Signal words: choose, select, committee, team.
Fast decision test
Section titled “Fast decision test”- Am I splitting into separate cases, or moving through stages?
- If I swap the chosen objects, do I get a different outcome?
- Am I counting valid outcomes directly, or should I count the total and subtract bad cases later?