Permutations: Non Distinct Objects

Introduction

The term permutation can be defined simply as determining the number of all possible arrangements of a set of elements. Under permutation, arrangement falls into the Non-distinct objects category, which simply categorizes the objects that are indistinguishable, i.e., the objects have no distinction with other objects.

Permutation of Non-Distinct Objects

The permutation of non-distinct objects is the number of all possible arrangements of a set of non-distinct objects. In this scenario, all the possible elements are repeated.

For instance, let us consider that you have a container of non-particular balls which further has 4 balls inside it. When you are utilizing the term non-particular item, it will directly imply that each of the balls present inside the container is of the same size and the same weight. Additionally, it will also imply that each characteristic of one single ball is indistinguishable from all the other different balls present in the container. Thus, if you name the balls, for instance, as 1, 2, 3, and 4, and later attempt to get the balls, they will all look exactly the same as each other in their qualities.

On the other hand, let us assume that you make an attempt to get a ball from the container without taking a look at it. This will leave you with no option to differentiate between the different balls. Subsequently, every time you try and get any of the balls, it will consistently be something very similar according to your point of view.

This is why we use permutations to arrange non-distinct objects.

If there are n elements in a set and r1, r2, r3, r4, and so on till rk that are all alike and indistinguishable, then the number of possible arrangements of the same set is given as the following: 

n! / (r1! r2! r3! r4! …. rk!)

Conclusion

Therefore, we understand that permutation of non-distinct objects is the number of all possible arrangements of a set of non-distinct objects.