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:

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