Permutation and Combination Calculator

Your details

Without repetition: each item used at most once. With repetition: items can repeat. Circular: arrangements around a ring where rotations are identical.
The size of the full set you are choosing from.
How many items you pick or arrange. Must be a non-negative integer.
Permutations P(n, r)
20

Ordered arrangements (order matters, no repetition)

Combinations C(n, r)10
P / C ratio (= r!)2
P(n,r) no repeat20
C(n,r) no repeat10
P with repetition25
C with repetition15

P(5, 2) = 20 ordered arrangements; C(5, 2) = 10 unordered selections.

  • There are 2 times as many permutations as combinations (that factor is r!).
  • Allowing repetition gives 25 ordered and 15 unordered arrangements.
  • Around a circle, 10 distinct arrangements exist (rotations are considered identical).

Next stepIf items can repeat (e.g. a PIN with repeated digits or a buffet plate with repeated food), switch to a with-repetition mode above.

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