How many permutations can be formed by choosing r objects from n distinct objects?

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combinatorics Figure 1: Ferrers' partitioning diagram for 14.

In combinatorics, a permutation refers to the arrangement of objects where the order of selection is a factor. When choosing $r$ objects from a set of $n$ distinct objects, the number of possible permutations is denoted by the symbol $_{n} P_{r}$ (or $_{n} P_{k}$ using $k$ as the variable).

The formula to calculate the number of permutations is:

$_{n} P_{r} = \frac{n!}{(n - r)!}$

In this expression, $n!$ represents the factorial of $n$ , which is the product of all consecutive positive integers from 1 up to $n$ . This counting formula allows you to determine the total number of ordered arrangements without needing to list each one individually.1