# Combinatorics

### Combinatorial Concepts

In all combinatorial problems, there are several key concepts that must be distinguished:

#### 1. Population

The population is the set of elements that is being studied. The number of elements of this set is denoted by the letter **n**.

#### 2. Sample

The sample is a subset of the population. The number of elements of a sample is denoted by the letter **k**.

The samples are determined by two aspects:

**1.Order**

If the order matters there are permutations.

If the order does not matter there are combinations.

2.**Repetition**

If the elements are repeated there are permutations with repetition or combinations with repetition.

### Factorial of a Natural Number

The factorial of a natural number is the product of "n" consecutive factors from “n” to 1. The factorial of a number is denoted by **n!**.

#### Example

Calculate the factorial of 5.

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