# Find the number of permutations

The mathematics section is combinatorics, which studies the selection and arrangement of elements from a certain basic set in accordance with specified rules. Formulas and principles of combinatorics are used in probability theory to calculate the probability of random events and, accordingly, to obtain the laws of distribution of random variables. The number of permutations is the number of different ways in which a given set consisting of n elements can be ordered. Combinatorics allows you to determine the number of possible scenarios.

.**Find the number of permutations**

**n =**

**The number of permutations with repetitions**

**n =**

**k**

_{1}=**k**

_{2}=**k**

_{3}=**k**

_{4}=**k**

_{5}=## Example of a permutation

An example of all permutations of 3 objects. According to the formula, there should be exactly 6 of them.

P

_{3}=3!=1⋅2⋅3=6

With the increase in the number of objects, the number of permutations grows very quickly and it becomes difficult to depict them visually. For example, the number of permutations of 6 items is 720