Convertools

Permutations (nPr) Reference Values

Calculate the number of ordered permutations using nPr for integers with 0 ≤ r ≤ n ≤ 18.

Author

Prof. Hans Muller

Math editorial contributor

German renewable energy engineer at TU Munich, pioneering grid-scale hydrogen storage solutions

Reviewed for accuracy by

Prof. Kenji Tanaka

Math content reviewer

Japanese materials scientist at Kyoto University, known for breakthroughs in sustainable polymer research

Last updatedFebruary 22, 2026

PublishedFebruary 22, 2026

Table of Contents

  1. All value pages
  2. Reference table
  3. FAQs
  4. Methodology and review
  5. Related conversions

Reference Value Index

This page lists 84 reference values for quick browsing and lookup.

Back to converter page · View HTML sitemap

All Reference Values

Reference Table

Permutations (nPr) reference values
ScenarionPr
3 n n; 0 r r1 Permutation Count
3 n n; 1 r r3 Permutation Count
3 n n; 2 r r6 Permutation Count
3 n n; 3 r r6 Permutation Count
4 n n; 0 r r1 Permutation Count
4 n n; 1 r r4 Permutation Count
4 n n; 2 r r12 Permutation Count
4 n n; 3 r r24 Permutation Count
4 n n; 4 r r24 Permutation Count
5 n n; 0 r r1 Permutation Count
5 n n; 1 r r5 Permutation Count
5 n n; 2 r r20 Permutation Count
5 n n; 3 r r60 Permutation Count
5 n n; 4 r r120 Permutation Count
5 n n; 5 r r120 Permutation Count
6 n n; 0 r r1 Permutation Count
6 n n; 1 r r6 Permutation Count
6 n n; 2 r r30 Permutation Count
6 n n; 3 r r120 Permutation Count
6 n n; 4 r r360 Permutation Count
6 n n; 5 r r720 Permutation Count
6 n n; 6 r r720 Permutation Count
7 n n; 0 r r1 Permutation Count
7 n n; 1 r r7 Permutation Count
7 n n; 2 r r42 Permutation Count
7 n n; 3 r r210 Permutation Count
7 n n; 4 r r840 Permutation Count
7 n n; 5 r r2,520 Permutation Count
7 n n; 6 r r5,040 Permutation Count
7 n n; 7 r r5,040 Permutation Count
8 n n; 0 r r1 Permutation Count
8 n n; 1 r r8 Permutation Count
8 n n; 2 r r56 Permutation Count
8 n n; 3 r r336 Permutation Count
8 n n; 4 r r1,680 Permutation Count
8 n n; 5 r r6,720 Permutation Count
8 n n; 6 r r20,160 Permutation Count
8 n n; 7 r r40,320 Permutation Count
8 n n; 8 r r40,320 Permutation Count
9 n n; 0 r r1 Permutation Count
9 n n; 1 r r9 Permutation Count
9 n n; 2 r r72 Permutation Count
9 n n; 3 r r504 Permutation Count
9 n n; 4 r r3,024 Permutation Count
9 n n; 5 r r15,120 Permutation Count
9 n n; 6 r r60,480 Permutation Count
9 n n; 8 r r362,880 Permutation Count
9 n n; 9 r r362,880 Permutation Count
10 n n; 0 r r1 Permutation Count
10 n n; 1 r r10 Permutation Count
10 n n; 2 r r90 Permutation Count
10 n n; 3 r r720 Permutation Count
10 n n; 4 r r5,040 Permutation Count
10 n n; 5 r r30,240 Permutation Count
10 n n; 6 r r151,200 Permutation Count
10 n n; 9 r r3,628,800 Permutation Count
10 n n; 10 r r3,628,800 Permutation Count
12 n n; 0 r r1 Permutation Count
12 n n; 1 r r12 Permutation Count
12 n n; 2 r r132 Permutation Count
12 n n; 3 r r1,320 Permutation Count
12 n n; 4 r r11,880 Permutation Count
12 n n; 5 r r95,040 Permutation Count
12 n n; 6 r r665,280 Permutation Count
12 n n; 11 r r479,001,600 Permutation Count
12 n n; 12 r r479,001,600 Permutation Count
15 n n; 0 r r1 Permutation Count
15 n n; 1 r r15 Permutation Count
15 n n; 2 r r210 Permutation Count
15 n n; 3 r r2,730 Permutation Count
15 n n; 4 r r32,760 Permutation Count
15 n n; 5 r r360,360 Permutation Count
15 n n; 6 r r3,603,600 Permutation Count
15 n n; 14 r r1,307,674,368,000 Permutation Count
15 n n; 15 r r1,307,674,368,000 Permutation Count
18 n n; 0 r r1 Permutation Count
18 n n; 1 r r18 Permutation Count
18 n n; 2 r r306 Permutation Count
18 n n; 3 r r4,896 Permutation Count
18 n n; 4 r r73,440 Permutation Count
18 n n; 5 r r1,028,160 Permutation Count
18 n n; 6 r r13,366,080 Permutation Count
18 n n; 17 r r6,402,373,705,728,000 Permutation Count
18 n n; 18 r r6,402,373,705,728,000 Permutation Count

Frequently Asked Questions

Frequently asked questions for Permutations (nPr) and its reference values.

What does the Permutations (nPr) calculator do?

It helps with counting ordered arrangements in combinatorics, scheduling, and coding interviews.

What formula does the Permutations (nPr) calculator use?

nPr = n! / (n-r)! for ordered selections.

What inputs are valid?

n and r must be integers with 0 ≤ r ≤ n ≤ 18.

When would I use this?

counting ordered arrangements in combinatorics, scheduling, and coding interviews

Methodology and Review

Each row on this page links to a value detail page derived from the same conversion data file as the main calculator and reference table. This reduces inconsistencies across page variants.

Editorial metadata and structured data are rendered across the converter page and linked value pages. Review policies are documented in our review process and editorial policy.