**Definition:** Combinatorics is a branch of mathematics about the selection and deployment of elements of a set based on some conditions

Selected (or available) group of elements called **compounds**

## Permutations

**Definition:** Permutations of the different elements are called finite ordered set (that is, such sets that specify the order of elements) can be removed from a set containing elements (if all elements of a given set of different — get permutations without repetitions, but if in the given set elements may be repeated, then get the permutations with repetitions)

### Formula for the number of permutations

#### Without repetition

where (read "n factorial")

For (by definition)

**Example.** The number of different six-digit numbers can be formed from the digits without repeating the numbers in one number equal to

#### With repetitions

where

**Example.**The number of different six-digit numbers can be formed from three twos, two sevens and one five

(considered )