Difference Between Permutation and Combination

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

Permutation	Combination
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.

ⁿP_r = 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.

ⁿC_r = 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.

ⁿP_r =r! × ⁿC_r

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