Permutations (nPr)
Calculate the number of ordered permutations using nPr for integers with 0 ≤ r ≤ n ≤ 18.
Table of Contents
9 n n; 3 r r =
504 Permutation Count
Representative value from the Permutations (nPr) reference table.
Reference Values
Browse 84 reference values with individual detail pages for quick lookup.
Permutations (nPr)
Calculate the number of ordered permutations using nPr for integers with 0 ≤ r ≤ n ≤ 18.
Calculated Result
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Reference Table
Use this complete table for quick lookup and internal linking to specific value pages.
| Scenario | nPr |
|---|---|
| 3 n n; 0 r r | 1 Permutation Count |
| 3 n n; 1 r r | 3 Permutation Count |
| 3 n n; 2 r r | 6 Permutation Count |
| 3 n n; 3 r r | 6 Permutation Count |
| 4 n n; 0 r r | 1 Permutation Count |
| 4 n n; 1 r r | 4 Permutation Count |
| 4 n n; 2 r r | 12 Permutation Count |
| 4 n n; 3 r r | 24 Permutation Count |
| 4 n n; 4 r r | 24 Permutation Count |
| 5 n n; 0 r r | 1 Permutation Count |
| 5 n n; 1 r r | 5 Permutation Count |
| 5 n n; 2 r r | 20 Permutation Count |
| 5 n n; 3 r r | 60 Permutation Count |
| 5 n n; 4 r r | 120 Permutation Count |
| 5 n n; 5 r r | 120 Permutation Count |
| 6 n n; 0 r r | 1 Permutation Count |
| 6 n n; 1 r r | 6 Permutation Count |
| 6 n n; 2 r r | 30 Permutation Count |
| 6 n n; 3 r r | 120 Permutation Count |
| 6 n n; 4 r r | 360 Permutation Count |
| 6 n n; 5 r r | 720 Permutation Count |
| 6 n n; 6 r r | 720 Permutation Count |
| 7 n n; 0 r r | 1 Permutation Count |
| 7 n n; 1 r r | 7 Permutation Count |
| 7 n n; 2 r r | 42 Permutation Count |
| 7 n n; 3 r r | 210 Permutation Count |
| 7 n n; 4 r r | 840 Permutation Count |
| 7 n n; 5 r r | 2,520 Permutation Count |
| 7 n n; 6 r r | 5,040 Permutation Count |
| 7 n n; 7 r r | 5,040 Permutation Count |
| 8 n n; 0 r r | 1 Permutation Count |
| 8 n n; 1 r r | 8 Permutation Count |
| 8 n n; 2 r r | 56 Permutation Count |
| 8 n n; 3 r r | 336 Permutation Count |
| 8 n n; 4 r r | 1,680 Permutation Count |
| 8 n n; 5 r r | 6,720 Permutation Count |
| 8 n n; 6 r r | 20,160 Permutation Count |
| 8 n n; 7 r r | 40,320 Permutation Count |
| 8 n n; 8 r r | 40,320 Permutation Count |
| 9 n n; 0 r r | 1 Permutation Count |
| 9 n n; 1 r r | 9 Permutation Count |
| 9 n n; 2 r r | 72 Permutation Count |
| 9 n n; 3 r r | 504 Permutation Count |
| 9 n n; 4 r r | 3,024 Permutation Count |
| 9 n n; 5 r r | 15,120 Permutation Count |
| 9 n n; 6 r r | 60,480 Permutation Count |
| 9 n n; 8 r r | 362,880 Permutation Count |
| 9 n n; 9 r r | 362,880 Permutation Count |
| 10 n n; 0 r r | 1 Permutation Count |
| 10 n n; 1 r r | 10 Permutation Count |
| 10 n n; 2 r r | 90 Permutation Count |
| 10 n n; 3 r r | 720 Permutation Count |
| 10 n n; 4 r r | 5,040 Permutation Count |
| 10 n n; 5 r r | 30,240 Permutation Count |
| 10 n n; 6 r r | 151,200 Permutation Count |
| 10 n n; 9 r r | 3,628,800 Permutation Count |
| 10 n n; 10 r r | 3,628,800 Permutation Count |
| 12 n n; 0 r r | 1 Permutation Count |
| 12 n n; 1 r r | 12 Permutation Count |
| 12 n n; 2 r r | 132 Permutation Count |
| 12 n n; 3 r r | 1,320 Permutation Count |
| 12 n n; 4 r r | 11,880 Permutation Count |
| 12 n n; 5 r r | 95,040 Permutation Count |
| 12 n n; 6 r r | 665,280 Permutation Count |
| 12 n n; 11 r r | 479,001,600 Permutation Count |
| 12 n n; 12 r r | 479,001,600 Permutation Count |
| 15 n n; 0 r r | 1 Permutation Count |
| 15 n n; 1 r r | 15 Permutation Count |
| 15 n n; 2 r r | 210 Permutation Count |
| 15 n n; 3 r r | 2,730 Permutation Count |
| 15 n n; 4 r r | 32,760 Permutation Count |
| 15 n n; 5 r r | 360,360 Permutation Count |
| 15 n n; 6 r r | 3,603,600 Permutation Count |
| 15 n n; 14 r r | 1,307,674,368,000 Permutation Count |
| 15 n n; 15 r r | 1,307,674,368,000 Permutation Count |
| 18 n n; 0 r r | 1 Permutation Count |
| 18 n n; 1 r r | 18 Permutation Count |
| 18 n n; 2 r r | 306 Permutation Count |
| 18 n n; 3 r r | 4,896 Permutation Count |
| 18 n n; 4 r r | 73,440 Permutation Count |
| 18 n n; 5 r r | 1,028,160 Permutation Count |
| 18 n n; 6 r r | 13,366,080 Permutation Count |
| 18 n n; 17 r r | 6,402,373,705,728,000 Permutation Count |
| 18 n n; 18 r r | 6,402,373,705,728,000 Permutation Count |
Frequently Asked Questions
Common questions about Permutations (nPr), formulas, and typical use cases.
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
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