Key Concepts & Glossary
Key Equations
number of permutations of distinct objects taken at a time | |
number of combinations of distinct objects taken at a time | |
number of permutations of non-distinct objects |
Key Concepts
- If one event can occur in ways and a second event with no common outcomes can occur in ways, then the first or second event can occur in ways.
- If one event can occur in ways and a second event can occur in ways after the first event has occurred, then the two events can occur in ways.
- A permutation is an ordering of objects.
- If we have a set of objects and we want to choose objects from the set in order, we write .
- Permutation problems can be solved using the Multiplication Principle or the formula for .
- A selection of objects where the order does not matter is a combination.
- Given distinct objects, the number of ways to select objects from the set is and can be found using a formula.
- A set containing distinct objects has subsets.
- For counting problems involving non-distinct objects, we need to divide to avoid counting duplicate permutations.
Glossary
- Addition Principle
- if one event can occur in ways and a second event with no common outcomes can occur in ways, then the first or second event can occur in ways
- combination
- a selection of objects in which order does not matter
- Fundamental Counting Principle
- if one event can occur in ways and a second event can occur in ways after the first event has occurred, then the two events can occur in ways; also known as the Multiplication Principle
- Multiplication Principle
- if one event can occur in ways and a second event can occur in ways after the first event has occurred, then the two events can occur in ways; also known as the Fundamental Counting Principle
- permutation
- a selection of objects in which order matters