Permutation with Replacement Calculator

Permutations PR(n,r)
Find PR(n,r) where:
PR(n,r) = nr

n =
r =
Answer:
PR(n,r) = nr

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Calculate the permutations for PR(n,r) = nr. For n >= 0, and r >= 0.

If we choose r elements from a set size of n, each element r can be chosen n ways.  So the entire sequence of r elements, also called a string, can be chosen in n x n x n x n ..... x n = nr ways.

Permutation Replacement Formula:

PR(n,r) = nr

Examples

Choosing Letters from an Alphabet

If we want to choose a sequence of 2 letters from an alphabet size of 4 letters {a,b,c,d}, the number of permutations, with replacement allowed and where the order counts, is PR(4,2) = 42 = 16. Namely {a,a}, {a,b}, {a,c}, {a,e}, {b,a}, {b,b}, {b,c}, {b,d}, {b,a}, {b,b}, {b,c}, {b,d}, {b,a}, {b,b}, {b,c}, {b,d}.

If we want to choose a sequence of 20 letters from an alphabet size of 4 letters {a,b,c,d}, the number of permutations, with replacement allowed and where the order counts, is PR(4,20) = 420 = 1.0995 E+12 possible ways.

Rolling Dice

Let's say we want to roll a die 60 times and record our sequence of 60 results such that it is our sequence of elements. Therefore, we are choosing a sequence of 60 dice rolls from a set size of 6 possible numbers for each roll, using one common six sided die. {1,2,3,4,5,6}.

PR(6,60) = 660 = 4.887367798 E+46 possible ways to create that sequence of 60 dice rolls.

References

For more information on permutations and combinations please see http://mathworld.wolfram.com/Permutation.html

 

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Furey, Edward "Permutation with Replacement Calculator" From http://www.CalculatorSoup.com - Online Calculator Resource.