In this topic of Counting Techniques, we will read and compare **permutations** and **combinations** on counting and types of counting and discuss their formulas and numerical.

## Define Counting Technique in statistic?

In some cases, the sample or event space is so large that it isnâ€™t feasible to write it out. Mathematical tools can be useful to count the size of the sample space and event space in that case. Such tools are called counting techniques.

### Types of Counting Techniques in Mathematical Method

There are two types of counting techniques.

- Permutation Technique
- Combination Technique

### What is Meant by the Permutation Technique?

In the mathematical method, the number of ways to **arrange **things is called a permutation.

#### For Example:

Arranging people, digits number of anything, letters, and color are examples of permutation.

### What is called Combination?

In the mathematical method, the number of ways to **choose** things is called a Combination.

#### For Example:

An example of a combination is any cricket team.

For example, if a team coach has 16 team members, then he selects 11 out of these 16 members. This process of choosing is called a combination.

### Concept Of Permutation and Combination

The simple concept of permutation and combination is given in the form of graphs below.

### Cases of Permutaion

There are three types of cases of permutation.

- Repetition is allowed
- Repetition is not allowed
- Distinct Permutation (when they are not all difference)

#### Define Repetition is Allowed

Repetition is allowed: when a single word, or a group of words, is repeated for effect.

#### Formula for Repetition is Allowed

#### for example:

when tossing two coins. and the result is

HH, HT, TH, TT

#### Define Repetition is not allowed

Repetition is not allowed: when a single word, or a group of words, is not repeated for effect.

#### Formula for Repetition is not allowed

#### For Examples

when tossing two coins. and the result is

HH, HT, TH, TT