Permutation with Repetition Table (n^r)
Build a table of permutations with repetition, n to the power r, across a range of n and r values. Enter the maximum n and maximum r to see every value at once.
Input
See the values of permutations with repetition, n to the power r, across a range of n and r in one table. Enter a maximum n and a maximum r.
Largest n shown as rows
Largest r shown as columns
Result
Value when n is 6 and r is 6
46,656
Permutation with repetition table
Each cell is n to the power r. Rows are the number of kinds n and columns are the count r.
| n and r | r = 0 | r = 1 | r = 2 | r = 3 | r = 4 | r = 5 | r = 6 |
|---|---|---|---|---|---|---|---|
| n = 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| n = 2 | 1 | 2 | 4 | 8 | 16 | 32 | 64 |
| n = 3 | 1 | 3 | 9 | 27 | 81 | 243 | 729 |
| n = 4 | 1 | 4 | 16 | 64 | 256 | 1,024 | 4,096 |
| n = 5 | 1 | 5 | 25 | 125 | 625 | 3,125 | 15,625 |
| n = 6 | 1 | 6 | 36 | 216 | 1,296 | 7,776 | 46,656 |
The number of permutations with repetition equals n to the power r, arranging r items in order from n kinds with repeats allowed.
How it works
- A permutation with repetition counts the ways to arrange r items in order from n kinds when repeats are allowed, and equals n to the power r.
- When r is 0 there is exactly one arrangement, the empty one, so every n gives a value of 1.
- In this table each row is the number of kinds n and each column is the count r, and each cell shows n to the power r.
- Big integers are used internally so the values stay exact even when they grow very large.
- Upper limits are placed on the maximum n and maximum r to keep the table readable.
Reviews
Tell us what you think of this calculator.
Write a review
- Home
Permutation with Repetition Table (n^r)