Permutations Calculator

Calculate ordered permutations P(n, r), circular arrays, repeating subsets, and multiset word anagram frequencies in high precision.

728x90

Total Items (n)

Arrange Items (r)

Arranging 3 items in strict sequential order.

Total Unique Ordered Arrangements

720

There are exactly 720 unique arrangements possible.

📂 Mathematical Substitution Steps

Formula: P(n, r) = n! / (n - r)!

Substitute: P(10, 3) = 10! / (10 - 3)! = 10! / 7!

Numerator (10!): 3628800

Denominator ((7)!): 5040

Result: P(10, 3) = 720

728x90

Combinations vs Permutations

The fundamental core difference between Combinations and Permutations boils down to order.

In Permutations, the relative sequence or sequencing order matters (such as credentials passcode sequences). In Combinations, order is completely irrelevant, and only the unique elements of the chosen subset matter (like picking cards in a hand).

Combinations (nCr)

{A, B} equals {B, A}

Permutations (nPr)

(A, B) is distinct from (B, A)

Common FAQs

What does standard nPr signify?

nPr stands for the number of ordered arrangements possible when selecting 'r' items from a pool of 'n' total options.

When should I use Multiset Permutations?

Multiset formulas are applied when the source set contains repeating elements (like the word 'APPLE' containing two 'P's) to avoid double-counting identical arrangements.

What are circular permutations?

Circular permutations arrange items in a continuous loop. Since rotating the loop doesn't change relative neighbors, there is no designated 'first' position, making the formula (n - 1)!.