Understanding Permutations (nPr)

Permutations calculate the number of possible arrangements of r items from a set of n items where order matters. This is fundamental in probability, statistics, and combinatorics for solving problems involving arrangements, rankings, and ordered selections.

Calculation Formula

The formula for permutations is: nPr = n! / (n - r)!

Where "!" denotes factorial (e.g., 5! = 5 × 4 × 3 × 2 × 1 = 120).

Example Calculation

For n=5 and r=3: 5P3 = 5! / (5-3)! = 120 / 2 = 60 possible arrangements.

This means there are 60 ways to arrange 3 items from a set of 5 when order matters (e.g., ranking the top 3 contestants from 5 participants).

Reference Table

n	r	nPr
4	2	12
6	3	120
8	2	56

Tips & Notes

n and r must be non-negative integers with r ≤ n.
For large values (n > 170), factorials may exceed JavaScript's number precision.
Use the permutation generator only for small n (≤8) to avoid performance issues.

Frequently Asked Questions

What is the difference between permutations and combinations?

Permutations (nPr) consider order, while combinations (nCr) do not. For example, arranging 3 books on a shelf uses permutations, while selecting 3 books from a pile uses combinations.

Can n and r be decimal numbers?

No, n and r must be non-negative integers. Decimal values will be truncated to integers.

How are large factorials handled?

For n > 170, JavaScript cannot represent factorials exactly due to floating-point limits. The calculator uses iterative multiplication to compute nPr without directly calculating large factorials when possible.

Permutation (nPr) Calculator

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Permutation nPr Calculator - Arrange With Order

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