# How Permutation And Combination Are Relevant In Mathematics?

**Introduction:** People often need to choose a certain number from a large set. Many may say that this depends completely on luck and there is no reasoning. But in mathematics, you can calculate the number of ways you can choose this number. For that, you need to learn the chapter known as permutation and combination. Here, the students have to make many subsets of the choices. The concept of permutation is a bit different from that of combination. It allows you to calculate what are the chances of forming a particular event from random sources. Read this article to know the chapter more.

## The idea of permutation:

Suppose there are 3 numbers and you have to choose a pair. A permutation is a process in which you can select all the available options from this. You get to arrange the entire set of numbers into a sequence. It gives the user an idea of how many numbers of options they can select from this process. It allows people to comprehend the number of choices available to them. For this, you need a finite set and make these orders. There are mainly two types that fall into this category:

**1) Repetitive:** There are cases where you have to select the same number again and again. For example, there is a four-digit number present. Here you may have to find how many times the number ‘3’ can appear in it. For this, you just find in each of the 4 digits the number of times ‘3’ can appear. You can use simple formulae (n * r) where n is the number of times a person has to select. R is the short form of the term repetition.

**2)Without repetition:** There is no fixed order in which you have to select here. When you choose one part of the option, you take out one option from the entire set. There is no chance for repetition in this process as it can happen only once.

## The concept of Combination:

This is a process in which you can select the items without worrying about the order. Here AB means the same as the order of BA. You can take as many options as you can at one time. You don’t have to subtract the number of chances you can take. A simple way to understand is to form a two-digit number with ‘2’, ‘3’, and ‘4’. Here you can take as many combinations as you want, such as (2,3,4), (2,4,3),(3,4,2), etc. In this concept, the simplest way to find it is with the factorial of 3. The number of combinations you can have is 6.

### Difference between the two:

You need to identify the feature of each concept before proceeding with the sum. Go through these differences for a brief idea:

- The concept of permutation is mainly used to get a sequential order. For example, when you have to arrange digits or numbers you will use this method. In combination, you have to choose an item from a large set. There is no point in deciding the order in this category.
- For permutation, on the other hand, order is the most important thing. It is because you have to arrange the objects in a particular way. Here the order will change the meaning of the entire option.
- When there is one combination, the kids can get a large number of permutations from it. But when it comes to one permutation, you can derive only one combination.

The chapter or permutation and combination does not have just one type of problem. Each of the problem sums has a different approach and thinking. Learn math online from sites such as Cuemath to understand this chapter.