📊 Permutations

Counting and arrangement problem

Determine the number of ways to arrange objects where the order matters.

Theory:

The number of ways to arrange $r$ objects from a set of $n$ distinct objects is given by:

$$P(n,r)=\frac{n!}{(n-r)!}$$

Where:

• $n$ : Total number of distinct objects
• $r$ : Number of objects to arrange

Multisets (Permutations with Repetition):

If some elements are repeated, the number of distinct permutations is given by:

$$\frac{n!}{k_1!k_2!\dots k_m!}$$

Where $k_1,k_2,\dots ,k_m$ represent the frequencies of the repeated elements.