Permutation
A permutation is an ordered arrangement of r items chosen from a set of n, calculated as n factorial divided by (n − r) factorial, used whenever the selection order matters.
See it move
A permutation counts ordered arrangements, used whenever sequence matters. Ranking a first-choice, second-choice and third-choice supplier from 6 shortlisted suppliers gives P(6,3) = 6 factorial ÷ (6 − 3) factorial = 720 ÷ 6 = 120 possible rankings, because swapping which supplier is first versus second creates a genuinely different outcome. Whenever a question could start with 'in what order', permutation is the right count, not combination.
The formula
Variables
- Total number of items available
- Number of items arranged (selected in order)
- Number of ordered arrangements
Counts the number of ordered arrangements of r items chosen from a set of n.
Check yourself
A sales manager wants to assign 3 of 5 shortlisted reps to a ranked Gold, Silver and Bronze incentive tier. How many ways can this ranked assignment be made?