Concept of Combination and permutation & it’s Calculations

Suppose you are offered a basket full of different fruits an asked to pick up only avocado, raspberry and strawberries from it.  How are going to pick them up? Would you consider, to pick them according to the alphabetical order or the order in which they are called in front of you?

Most probably, while picking up fruits you will never consider the order, you just pick them which comes first in front of your eyes. This random picking up of objects (fruits) from a pile of other objects is known as combination. While on the other hand if you choose to pick fruits on the basis of their size i.e. first raspberry and avocado at the last, considering any specific order it is termed as permutation. 

To learn more about the concepts of combinations and permeation in detail and how to calculate them using their distinct formulas consider the article below.

The Concept of Combination

A combination is just a technique of picking certain things from a given collection of objects in such a way that the sequence of their selection doesn’t matter. In combinations, it is also expected that any single variable cannot be chosen more than once i.e. repetition of values/objects is not permitted in combinations.

In order to define combinations in exact mathematical terms, we would say, a combination is a subset of a bigger set, which doesn’t matter the order of the elements during the new subset compilation.

As mentioned, the order of items does not have to be considered while forming the combinations. Only the selection or the insertion of items is significant in combinations, and not the arrangement of them with relation to the other chosen items.

How to calculate Combination

To calculate how many possibilities are there, in order to form the combination, the formula mentioned below can be used:

nCr = n! /r! (n−r)!

By using that formula with technology, the Modern online number combination calculator help us to achieve that combinations of numbers easily.

Let’s first elaborate the left side of the formula, the term nCr. That implies we will be picking r things from a collection of n objects. Whereas the C represents the abbreviation for the combinations.

The remaining formula is quiet simple in the same manner. Where n! is the number N factorial, shown by n!, 1 i.e. 1.2.3….. (n-2). (n-1).n. When using the exclamation point “!”, remember that it indicates factorial, (the product of that number and all positive integers less with it). 

Moreover, for physical reasons, this is only applicable when n>r. Assume the n<r. Then the above term must show the various methods to choose two items (i.e. n=1 and r=2) from a collection of one. This cannot be made possible physically, however. All expressions with n<r are therefore specified as nCr  = 0.

Concept of Permutation

Permutation is a method of selection that considers the sequence of items during selection.  Permutation may be described simply as the number of possibilities to arrange a few or all members into a specific order.

Therefore, the act of putting all the components of a set into some sequence or order is referred to as permutation. In other words, if the set is already sorted, the operation of permutation is called the rearrangement of its elements. 

Permutations appear in nearly every mathematical field, albeit in varying degrees. Many alternative orderings on finite sets give rise to the process of permutation. Moreover, the permutation can be further subdivided into two types i.e. the permutation with repetitions and without repetitions.

 Types of Permutation

How to Calculate Permutation

If there are ‘n’ number of items to select from ‘r’ number of things or group of things, then mathematically the permutation can be denoted as

nPr = n!/(n-r)!

However, to calculate the permutation, two separate methods are implied. The method to calculate the permutation are distinct on the occurrence of repetition or absence. 

Permutation with Repetition

The permutations can be, if r items of something is chosen from n kinds are:

n × n × … (r times)

It is usually straightforward to write using the r exponent as

nr = n x n…. (up to r times)

So, the basic formula could be stated as

nr 

Permutation without Repetition

The formula for permutation used when the repetition is not considered during selecting items is given as

P = n!/(n−r)!

Also you can calculate permutation without any repetition in numbers by using a permutation solver that provides result in all possible steps.