PERMUTATION of Non-Distinct Objects

In this section we will understand how to use Permutation when the objects or items are repeating i.e., the objects are non-distinct or similar. Our traditional concept of Permutation will not be applicable here. We have to modify the formula. Let’s see how to use it.

If you want to learn the basics of Permutation & Combination, click here. Only after getting the basic understanding of Permutation, proceed further.

Concept for Permutation of Non-Distinct Objects

When the number of objects or items are repeating, then we have to divide the traditional output of permutation with factorial of number of times the object is repeating. Suppose the object is repeating 2 times, then we have to divide by 2!. If the object is repeating 3 times, then we have to divide by 3!.

Example of Permutation of Non-Distinct Objects:

Example: COOL

Lets understand this in detail with a simple example. Refer the word “COOL”. This word is having 4 letters. If we apply the traditional Permutation, we will get our answer as 4!. (Click here to know how to use Permutation Formula).

But if you note, here the letter “O” is repeating 2 times. It means if we replace both the O’s with each other, no new word will be formed. It will be the repetition of the word. So, our traditional approach will not be applicable here.

To get the solution, we have to observe, how many letters are repeating or are non-distinct. Here letter “O” is repeating 2 times. So here we have to divide our traditional answer 4!, by 2!.

Basically, the concept is, in case of permutation of non-distinct objects, we have to divide the traditional output of permutation with factorial of number of times the object is repeating

Video Explanation

Refer the below video to understand the concept in more detail using ANIMATION & visual tools.

Some other examples of Permutation of Non-Distinct Objects:

Example: COOOL

Here in the word “COOOL”, the letter O is repeating 3 times. On applying traditional Permutation, the answer will be 5!. But here, “O” is repeating 3 times, so we have to divide the traditional answer, 5!, by 3!.

Example: INSTITUTE

Here in the word “INSTITUTE”, the letter I is repeating 2 times, and the letter T is repeating 3 times. On applying traditional Permutation, the answer will be 9!. But here, “I” is repeating 2 times, and T is repeating 3 times, so we have to divide the traditional answer by 2! & 3!.