Permutations Calculator (nPr)

Permutations nPr
Find P(n,r) where:
P(n,r) = n! / (n - r)!

n =
r =
P(n,r) =

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Calculator Use

Like the Combinations Calculator the Permutations Calculator will find the number of sub-sets that can be taken from a larger set. However, the order of the subset now matters. The Permutations calculator will find the number of sub-sets that can be created including sub-sets of the same items in different orders.

Permutations Formula:

P(n,r) = n! / (n - r)!

Calculate the permutations for P(n,r) = n! / (n - r)!. "The number of ways of obtaining an ordered subset of r elements from a set of n elements."[1]

Permutation Problem 1: At a High School Track meet the 400 meter race has 12 contestants. The top 3 will receive points for their team. How many different permutations are there for the top 3 from the 12 contestants?

For this problem we are looking for an ordered sub-set 3 contestants (r) from the 12 contestants (n). We must calculate P(12,3) in order to find the total number of possible outcomes for the top 3.

P(12,3) = 12! / (12-3)!=1,320 Possible Outcomes

Permutation Problem 2: An NFL team has the 6th pick in the draft, meaning there are 5 other teams drafting before them. If the team believes that there are only 10 players that have a chance of being chosen in the top 5, how many different orders could the top 5 be chosen?

For this problem we are finding an ordered sub-set of 5 players (r) from the set of 10 players (n).

P(10,5)=10!/(10-5)!= 30,240 Possible Orders


[1] For more information on permutations and combinations please see


Cite this content, page or calculator as:

Furey, Edward "Permutations Calculator nPr" From - Online Calculator Resource.