answersLogoWhite

0

Distinct permutations are the unique permutations of n objects taking r at a time when some of the objects are repeated. For a complete example read below.

First, you need to understand what permutations are. Suppose you have 3 balls, 2 of them blue and one red. Lets call the first blue ball, B1, second blue ball, B2, and the third ball (the red one) R1. Permutation of the three balls taking the three at a time is all the different ways you can arrange those three balls in a row. That number is 3! = 3x2x1 = 6. The arrangements are listed below.

1) B1,B2,R1

2) B1,R1,B2

3) B2,B1,R1

4) B2,R1,B1

5) R1,B1,B2

6) R1,B2,B1

Now, suppose you remove the subscripts. The list looks like this:

1) B,B,R

2) B,R,B

3) B,B,R

4) B,R,B

5) R,B,B

6) R,B,B

Note that you can't differentiate between 1 and 3, they looks like the same. Also, 5 and 6 looks the same, and 2 and 4 looks the same. So the only unique combinations seems to be 1,2 and 5. Those are call the distinct permutations.

To calculate the distinct permutations of n elements taking r at a time use the formula: nPr / (k1!*k2!*...*kn!)

In the example above:

nPr = 3! = 6 -> All permutations of n elements taking r at a time

k1 = 2 = 2 -> because we have two identical blue balls

k2 = 1 = 1 -> we only have one red ball.

So, distinct permutations = 3! / (2!*1!) = 6 /(2*1) = 3. Those distinct permutations are: BBR, BRB, RBB.

You can use a software, such as Wolfram Mathematica, to generate the distinct permutations using the function DistinctPermutations.

User Avatar

Wiki User

16y ago

What else can I help you with?

Related Questions

How do you make a good sentence with the word permutation?

i am a permutation is a awesome answer


What is the relationship between Permutation?

Permutation is when order matters


What is the definition of permutation?

A permutation is an ordered arrangement of a set of objects.


When was Permutation City created?

Permutation City was created in 1994.


How many pages does Permutation City have?

Permutation City has 310 pages.


What is the probability that a randomly selected permutation of the letters AABCSU would spell abacus?

To determine the probability of randomly selecting the permutation "abacus" from the letters AABCSU, we first calculate the total number of distinct permutations of the letters. The total permutations are given by the formula ( \frac{n!}{n_1! \cdot n_2! \cdots n_k!} ), where ( n ) is the total number of letters and ( n_i ) are the counts of each distinct letter. Here, we have 6 letters (2 A's, 1 B, 1 C, 1 S, 1 U), resulting in ( \frac{6!}{2!} = 360 ) distinct permutations. Since "abacus" is one specific permutation, the probability is ( \frac{1}{360} ).


Is every permutation always a one-to-one function?

By definition, a permutation is a bijection from a set to itself. Since a permutation is bijective, it is one-to-one.


What is the number of distinguishable permutation of the letters in the word September?

September has 9 letter, of which one appears 3 times. So the number of distinct permutations is 9!/3! = 120,960


When was Permutation - album - created?

Permutation - album - was created on 1998-06-01.


What is the permutation of 7?

There can be only one permutation of a single number: so the answer is 7.


Can a permutation be made with negative numbers?

Yes, a permutation can be made with negative numbers. In mathematics, a permutation is an arrangement of objects in a specific order. Negative numbers can be included in a permutation just like any other integer. The order in which the negative numbers are arranged would be considered a valid permutation.


What is a permutation of 36?

the answer is 1.856Etc.