This online Permutations Calculator computes the number of permutations P(n,k) given values of the parameters n and k, that must be non-negative integers. The calculations are performed using arbitrary-precision decimal arithmetic. The result is presented both in scientific notation and in the form of a long integer number.
P(n,k) = n! / (n-k)!
Permutations formula
The number of permutations \(P(n,k)\) is defined as the number of ways of obtaining an ordered subset of \(k\) elements from a set of \(n\) elements and given by the formula:
$${ P (n , k) }=\frac { n! }{ (n-k)! } .$$
For example, lets consider a running competition with 15 contestants. The runner, finished first, receives the gold medal, the runner, finished second, receives the silver medal and the runner, finished third, receives the bronze medal. How many different permutations are there for the top 3 from the 15 contestants?
For this problem we are looking for an ordered subset of 3 contestants (\(k\)) from the 15 contestants (\(n\)) taking place in the competition. So, we have to calculate \(P(15,3)\) in order to find the total number of possible outcomes for the top 3 runners. Using our Permutations Calculator it’s easy to find \(P(15,3)\) = 2730 possible outcomes.
This online calculator uses arbitrary-precision decimal arithmetic, so that you can get the exact value of the number of permutations even for a sufficiently large value of \(n\) within a reasonable time span (depending on the computational power of you computer).
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Check out our other statistics calculators such as Binomial Probability Calculator or Hypergeometric Distribution Calculator.