Permutation
There are numerous distinct interpretations associated with the concept of permutation in mathematics, all of which are linked to the process of permuting (rearranging) objects or values. To put it another way, a permutation is a collection of things that has been organized into a certain order.
A permutation is a sequenced selection of elements from a collection that is either performed repeatedly or without repetition. It is one of the most significant ideas in combinatorial analysis, and it is defined as, the permutation is a selection procedure in which the order of the selection criteria is important.
Permutation may be simply described as the number of different ways to arrange a small number of members or all of them in a certain order.
Permutation Formula
The number of permutations on ‘n’ distinct items taken ‘r’ at a time is the same as the number of various ways in which ‘r’ spaces may be filled up with the ‘n’ things that have been provided. It is indicated by the letters npr or p (n, r) and is represented by the formula:
Types of Permutation
The permutation, however, based on the arrangements done can be classified into three different types:

Repetition is permitted
In order to calculate the statistics of permutation (i.e., the number of different ways in which an arrangement may be accomplished), this formula is used when the repetition of values and objects is allowed. When the repetition in a permutation is allowed it is calculated using the formula n × n × n × ……(r times) = n^r

Repetition is not permitted / no repetition
While guaranteeing that there is no repetition, this method is used to calculate the statistics of permutation (the number of different ways in which an arrangement may be made). It may be done manually by using the formula of permutation or also by using online tools like permutation product calculator.

Permutation of multisets
It is a distinct type of permutation that doesn’t consider whether the reputation is occurring or not. Moreover, when the items to be permuted are not distinct, this type of permutation occurs. The permutation of multisets is calculated as n! / (P1! P2!….Pn!)
Difference between Combination and Permutation
The name ‘permutations and combinations’ refers to two related problems. The two counting options to pick from a number of elements. Where the range of selection is taken into consideration for permutations while it is neglected for combinations.
While counting numbers the combination and permutation are two important concepts and differentiating both of them from each other is really essential. To avoid confusion among both the concepts below is provided a brief description of combination and permutation.
Combination
Combinations are defined as the number of different ways in which a lower or equal number of items may be ordered or selected from a collection of things when the order in which the things are picked or arranged is not significant. Order, in contrast to permutations, does not matter in combination.
nCr or C(n, r) indicate the number of combinations of ‘n’ different items taken ‘r’ at a time. The combinations, however, can be mathematically denoted as nCr which we may calculate by using online combination calculator.
Permutation
A permutation is an arrangement in a certain sequence for all or portion of certain objects. The manner by which smaller or equal numbers of individuals or items in a group of individuals or collections are arranged or selected in due course as per the sequence of arrangement or selection is termed permutation.
Wrapping Up
Permutation and combination deal with counting procedures without mentioning the number of items in the specific set or the number of results of that specific experiment. Moreover, despite being quite similar in the matter are used in number counting their lies several differences among them. The order of numbers is highly considerable in permutation and comprises several different types. The combinations don’t take into consideration the order of numbers or elements in the data set to be counted.