Permutation Vs. Combination: So Similar But Yet So Different!

07 Apr 2022 1127 share it:

Permutation and combination, two terms that mean different but are still taken together whenever they are talked about. You might have heard your professor saying these terms multiple times. Have you ever wondered why so? Why these terms are used in a single sentence, and what differences they might have? If yes, then this blog will surely help you fulfill those queries, as in this one, you will learn about key differences between permutation and combination.

For those who do not know, permutation and combination represent a group of data in the form of sets and subsets. You can make multiple permutations and combinations to ensure that the data you have stored is represented sensibly. Both of these are said to be similar. However, they are different. Take a look below at their definitions for a better understanding.

Permutations - It refers to ordering the elements in a particular sequence to enhance clarity or usability of the data. When a set of data is relocated from its natural place it is called permuting the sequence. You try a lot of permutations to find an optimal state for the sequence. The order of the data makes a difference in this concept as if the order is changed, a new permutation is created.

Combinations - It is a common word that means to combine two like things. However, when it comes to the concept in mathematics, you will find that there are limitations to what is a combination and what is not. The combinations are formed where no entity is repeated and each has a logic of standing. The order of data used is of no significance in creating the combination.

Well, now that you have the basic idea of permutation and combination, we can move on to the theme of this blog, which is understanding the differences between the two and finding out various applications. Do not worry! We will not make this blog a lesson on the topic as for that you can read the samples by our experts.

Without further ado, let us first take a look at why students stay confused about the terms.

Permutation Vs Combination: Why Students Are Confused?

As you read above, the two terms have their differences, but they are considered a part of the same concept. While they are used in different contexts, the fact that these are termed together and have identical functionality makes it confusing for the students. According to the permutation and combination definition, a password is a permutation of numbers, while colors are combinations of two or more monochromes. However, thousands of students often confuse it and interchange the terminologies. You might have heard people ask "What is the combination of your lock?", while the correct use must be "What is the permutation for your lock?".

There are thousands of similar cases where the concepts are interchanged, and thus it creates a lot of confusion among the students. To help you avoid such confusion, check out the list of differences between the two.  

S.NO.	Permutations	Combination
1.	It is used to arrange entities such as  digits, colors etc.	A group or type of food, team, sports and other selections fall into this category.
2.	If you have to choose or move only one entity from a group, you can use permutations.	If you have to choose a number of specific entities in a set of data, combination is what you want to choose.
3.	Whenever you are worried about order, in terms of ranking, favoritism or any kind of series, permutation is your choice.	When you are worried about choosing entities irrespective of their order, when you just have to choose three things without their ranking or your favorite items, this is your choice to go.
4.	When you have to choose something specific from a bunch, you use permutation.	When your selection does not require anything specific and you are free to choose, combinations are made.

These are the key differences between permutation and combination, you can say that the working of both is similar to the role but they have significant relevance in the field. The differences in themselves are too similar to be cleared, and thus students often stay confused. You can ask experts for an in-depth comparison of the two entities if you feel that this is not enough to be completed.

You may also like to read: 5 Simple Techniques to Solve Tricky Mathematics Problems

How Do You Use Permutations And Combinations In Real Life?

There are so many applications of both of these concepts that can help you understand how they can be used in real life. Some of the key applications are -

1. While Choosing a Passcode- Each one of us has our smartphones, our emails, credit cards, and ATM cards safe with the help of a passcode. That code that you have chosen might seem like a combination of plain sight. However, when you understand the concept you will realize that the arrangement of those digits when changed completely messes up your code, and thus that is the most common application of permutation.

2. Food Menus - The menus at your favorite restaurants are made with a combination of some of the finest dishes from across the globe. It is the hotel owner’s choice to keep or remove a cuisine from the menu however changing them will not affect the menu, they will just reflect on the selection or you can say the combination of dishes that they serve or the ingredients that they use. One of the most commonly used things is the best example of combination.

3. Ranking School Kids- When it comes to calling for volunteers from, a classroom you make a combination of students, and when it comes to rankings in academics, one has to go for permutations. The difference is clear now while choosing a volunteer, the arrangement of the students is not important as they are all volunteers, but when ranking if you change the standings of the student, the result is changed. That is how these concepts work.

The permutations and combinations are endless for using these concepts in real life. Everything that revolves around the numbers or selection from a group is subjected to permutation and combinations in real life. You will find many other examples in the samples that are shared on our website by the experts simply log on to the page and start exploring the concept to its core.

By these uses, you also might have got an idea about what are the basic boundaries between the two. A lot of students also have queries related to how do you determine whether to use permutation or combination? Well, the applications suggest the use cases, when you are dealing with the arrangement of the entities, and it affects the meaning of the selection, you use permutations, and when it is just about selecting an entity, the term is used in combination. A single change in permutations causes disturbances to the arrangement while writing a single combination is not affected by how you use them. The best example of the use case is VIBGYOR. The combination of colors can be used in any arrangement as the result will be the same in the need however the arrangement of this can not be played with.

It is how one can differentiate in permutation vs combination. It is needless to say, they both are typically different from each other. The experts have tried to finish the explanation without going into deep technical terms as this is a blog to help you learn the concept. If you face issues in finishing papers on the subject, make sure you check out the next section.

You may also like to read: How to Solve Cubic Equations Using Factor Theorem and Graphs?

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