What is Permutation & Combination? List of Basic Formulas

Permutation and Combination are tough topics and sounds complicate to understand. With Permutation, every minute detail matter. At the same time, if we talk about the Combination, things are easy to manage. The details or order is not as much important like Permutation. In brief, Permutation is important for lists where order matters, and Combination is important for Groups where the order is not important.

What is Permutation?

The Permutation is defined as various ways in which objects can be selected from a given set and obviously order matters here. Take an example of salad, you are taking to your school. It contains tomatoes, radish, cucumber etc, this does not matter in which order they are arranged, the taste would be same in either case.

How about the PIN number that is generated by bank accounts? You have to be very careful about the order of numbers otherwise your request for money withdrawal would be rejected. This is important for your account accessibility otherwise invalid attempts could block your account. So, in any case, the order is important. The same is true for Permutation where every small detail has significance meaning and the order matters for the objects.

Permutation and combination havewider benefits for mathematics and engineering. They are used to sort algorithms in computer science. You just need to understand where the order of objects is necessary and where can you avoid it.

What is Combination?

Combinations are easy to understand when compared to Permutation and they are used when order doesn’t matter much. For a combination, the set ABC is similar to BCA. They are used for groups where you have to select items from a collection and order can be decided by yourself. Combination is defined as n number of things where k items are taken at a particular time without any repetition.

List of Basic Combination Formulas

There is a list of basic Combination Formulas to make the calculation of sets easier without any mistake. They can be put into the equation or you can sue them for a given set to derive the meaningful outcome without putting much focus on order.

\[\LARGE Combination = \:_{n}C_{r} = \frac{_{n}P_{r}}{n!}\]

When not related to Permutation,

\[\LARGE Combination = \:_{n}C_{r} = \frac{n!}{(n-r)!r!}\]

n, r are non negative integers
r is the size of each permutation.
n is the size of the set from which elements are permuted.
! is the factorial operator.

List of Basic Permutation Formulas

The biggest benefit of Permutation theory is game development where objects need to arrange logically like puzzle games, sorting games etc. Take an example of letters A, B, C, D, and E. based on permutation formula, there are 20 potential outcomes possible for these alphabets.

Each value of these 20 sets is named as permutation and the formula for its evaluation is – “nPk = n!/(n − k)!” Finding out permutation value for a given set is not easier still basic Permutation Formulas can help you in making things easier for you.

\[\large Permutation=\:_{n}P_{r}=\frac{n!}{(n-1)!}\]

\[\large Permutation\; with \;Repetition=n^{r}\]

Why do students need Permutation and combination?

A deep understanding of Permutation and Combination concepts allow you to make feasible for event programming. A good understanding is the basis of Probability and used everywhere to manage a group. If you are sure of concept in detail then it may create lots of confusion for you.So, the best idea is to study permutation and combination formulas carefully and apply them to real-life problems.