Permutation Coefficient Calculator

Instructions: You can use this permutation coefficient calculator to compute \(P_{n,k}\), for two given integers \(n\) and \(k\).

Type the integer \(n\):
Type the integer \(k\):

More about this Permutation Coefficient calculator for \(n\) and \(k\):

There are many Math contexts in which the use of permutation coefficients is relevant, especially in the calculation of probabilities using distribution probabilities or counting methods.

The formula for \(P_{n,k}\) is:

\[P_{n,k} = \frac{n!}{(n-k)!}\]

The idea of permutation is used to count the number of subgroups that can be formed when the ordering matters. For example, assume that in a group of 10 employees, we want to know in how many ways we can choose a president, vice-president and secretary, then we would use permutations because in this case the order of the assignment matters (Indeed, when you select 3 people, you still need to know which position each person will take). Concretely, the number of ways for the example would be \(P_{10,3} = \frac{10!}{(10-3)!} = \frac{10!}{3!}=\frac{3,628,800 }{6} = 720\)

For when order does not matter, then you need to use combinations instead

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