Difference Between Permutation and Combination

By Aina Parasher|Updated : June 21st, 2022

Difference Between Permutation and Combination: The difference between permutation and combination is that in permutation, the order of the members is taken into account, whereas in combination, the order of the members is irrelevant. For example, permutation is the arranging of objects or alphabets, whereas combination is the choosing of a group of objects or alphabets.

The permutation and combination formulas are useful for determining the difference between permutation and combination. In the upcoming sections, we will learn about the crucial aspects that will assist us in identifying the use and difference between permutation and combination.

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Difference Between Permutation and Combination

Both permutation and combination are fundamental aspects of counting. Counting numbers using pure reasoning is a major deal in and of itself. We can't address probability problems without counting. This is why we study permutations and combinations before probability. Here, we'll look at the difference between permutation and combination listed in the table below.

Key Difference Between Permutation and Combination

PermutationCombination
Permutation refers to the various methods of organizing a set of objects in sequential order.The combination is one of the numerous methods for selecting items from a big set of objects without regard for order.
It refers to the arrangement of objects.It does not indicate how objects are arranged.
The order/ sequence is really important.The sequence is completely unimportant.
Permutations are used for a variety of things.Combinations are used to describe comparable items.
Permutation can be done with or without the repetition of elements.Combination is not concerned with element repetition or lack thereof.

What is Permutation?

A permutation is a term that refers to the arrangement of a given collection of items in a specific order. The order of arranging is critical here. A basic example of permutation is if we have some objects with us and wish to organize them, how many ways can we arrange them?

A permutation is one of the various ways of arranging a few or all members in a certain sequence. It is the process of creating order from chaos. The permutations of r things taken from n things are equal to the factorial of n divided by the factorial of the difference between n and r.

nPr = n!/(n-r)!

What is Combination?

Combination is a method of selecting things from a large collection in such a way that the order of selection is irrelevant (non-similar Permutations). In lesser circumstances, we can assert that we will be able to count the number of Combinations. The combination is defined as the taking of n objects k at a time without repetitions. A Combination is the selection of r items from a set of n items with no replacement and where the order is irrelevant.

nCr = n!/r!.(n-r)!

Relation Between Permutation and Combination

"Permutation" and "Combination" are mathematical concepts that are connected. The combination is the counting of our picks from n things. Permutation, on the other hand, counts the number of arrangements from n objects.

Permutation and combination formulas can be combined to generate a single formula. The permutation of 'r' things picked from 'n' things is equal to the product of 'r' factorial and combination.

nPr =r! × nCr

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FAQs on Difference Between Permutation and Combination

  • The main difference between permutation and combination is that when the order/sequence of arrangement is required, permutations are employed. Combinations are used to determine the number of possible groups that can be formed.

  • If we are given 'n' items from which we want to organize 'r' elements, the number of potential arrangements or permutations is given by, nPr = n!/(n-r)!

  • If we have n elements from which to choose r elements, the number of possible combinations is given by,

    nCr = n!/r!.(n-r)!

  • Assume X and Y are two items that can only be ordered in two ways: XY or YX; this is known as a permutation. Now, if there is only one way to select X and Y, we select both of them to create a combination.

  • Permutation can be divided into three categories:

    • Permutation of n distinct things (when repetition is not allowed)
    • Repetition, where it is permitted.
    • Permutation, when the objects are not distinct. 

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