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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.

ByHoang TruongUpdated

See it move

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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.

Where it fits
TopicProbability & DistributionsCoreSubjectData Analysis & StatisticsCore

The formula

LaTeX
P(n,r)=n!(nr)!P(n,r) = \frac{n!}{(n-r)!}

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

PracticeCORE

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?

Select an answer to check your understanding.