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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 rr = 0r = 1r = 2r = 3r = 4r = 5r = 6
n = 11111111
n = 21248163264
n = 31392781243729
n = 41416642561,0244,096
n = 515251256253,12515,625
n = 616362161,2967,77646,656

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.

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