PEAZIT Aha card
Go straight to resources ↓A permutation fills every position in order
The first position has n choices, then n−1, and so on. Write n × (n−1) × … × 1 as n!.
| Relation | Meaning |
|---|---|
| 3 × 2 × 1 | After each choice, one fewer book remains. |
| 3! = 6 | The exclamation mark denotes factorial. |
| ABC, ACB, BAC, BCA, CAB, CBA | Listing all six orders checks the calculation. |
One worked example
- 3 × 2 × 1After each choice, one fewer book remains.
- 3! = 6The exclamation mark denotes factorial.
- ABC, ACB, BAC, BCA, CAB, CBAListing all six orders checks the calculation.
Watch out: The formula n! assumes distinct objects and every position filled. Indistinguishable repeated objects require adjustment.
Goal, prerequisites and card origin
What you will learn: Count arrangements of distinct objects.
What you need first: The multiplication rule.
An original PEAZIT working card. Independent expert review and effectiveness testing have not yet taken place. · v1
Show connections
The first position has n choices, then n−1, and so on. Write n × (n−1) × … × 1 as n!.