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!.

Factorial of a Natural Number

Factorial of a Natural Number

Example

Calculate the factorial of 5.

Factorial of 5