Explain Counting Technique with Permutation and Combination

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 isn’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.

difference between Permutation and Combination

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

examples of Repetition is allowed

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

Formula for Repetition is not allowed

For Examples

when tossing two coins. and the result is

HH, HT, TH, TT

examples of Repetition is not allowed

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