Permutation with exception/repetition

In summary, the conversation is about finding a formula to calculate permutations of a multiset, where redundant elements are allowed. The example provided involves creating a 3 digit number from a set of 5 numbers. The question is whether there is a formula for this scenario and if so, what it is.
  • #1
Crazorin
4
0
I need a formula to calculate permutation.
For example I have a 5 numbers and I creating a 3 digit number from it.
The numbers are: 1, 1, 1, 2, 3; I could write up 13 variations, but I couldn't work out the formula.
If the numbers are: 1, 1, 2, 2, 3 the number of variations are 18 (if I wrote them up properly)
Is there a formula to calculate this, or is it becoming too complex?
 
Mathematics news on Phys.org
  • #2
Crazorin said:
I need a formula to calculate permutation.
For example I have a 5 numbers and I creating a 3 digit number from it.
The numbers are: 1, 1, 1, 2, 3; I could write up 13 variations, but I couldn't work out the formula.
If the numbers are: 1, 1, 2, 2, 3 the number of variations are 18 (if I wrote them up properly)
Is there a formula to calculate this, or is it becoming too complex?

You're looking for permutations of a multiset (a set in which redundant elements are allowed).
(See https://en.wikipedia.org/wiki/Permutation#Permutations_of_multisets.)
 
  • #3
aikismos said:
You're looking for permutations of a multiset (a set in which redundant elements are allowed).
(See https://en.wikipedia.org/wiki/Permutation#Permutations_of_multisets.)

Thanks. It is almost what I need except in those example they use up all element of each set.
I would only use part of it. So if the sets are {1, 1}{2, 2}{3} then I have a total of 5 elements. And the question is how many different 3 digit numbers I can create of these 5 elements. Because they are numbers, the order matter so it would be a kind of permutation.
What would be the formula for that?
 

Related to Permutation with exception/repetition

1. What is a permutation with exception/repetition?

A permutation with exception/repetition refers to a rearrangement of a set of items where some elements are repeated and others are excluded from the arrangement. This means that the order of the items matters and there may be duplicates or missing elements in the final arrangement.

2. How is a permutation with exception/repetition different from a regular permutation?

A regular permutation is a rearrangement of a set of items without any restrictions, meaning that all elements are included and there are no duplicates in the final arrangement. On the other hand, a permutation with exception/repetition allows for some elements to be repeated and others to be excluded from the arrangement.

3. What is an example of a permutation with exception/repetition?

An example of a permutation with exception/repetition is the arrangement of letters in the word "MISSISSIPPI". Since there are four "I"s, two "S"s, and two "P"s, the final permutation would have 11 elements, with some letters repeated and others excluded from the arrangement.

4. How do you calculate the number of possible permutations with exception/repetition?

The number of possible permutations with exception/repetition can be calculated using the formula n!/(r1!*r2!*...*rk!), where n is the total number of items, and r1, r2, and so on represent the number of repetitions for each item type. In the example of "MISSISSIPPI", the number of permutations would be 11!/(4!*2!*2!)= 34,650.

5. What are some real-world applications of permutations with exception/repetition?

Permutations with exception/repetition can be used in various fields such as genetics, coding theory, and statistics. In genetics, it can be used to calculate the number of possible combinations of genes in a population. In coding theory, it can be used to generate unique codes or passwords. In statistics, it can be used to calculate probabilities in situations where certain elements are repeated or excluded from a sample space.

Similar threads

MHB #s of Combinations and Permutations of lines?
    • General Math
Replies
1
Views
732
MHB The number of possible permutations for the assessment
    • General Math
Replies
2
Views
2K
B Combinatorics and Magic squares
    • General Math
Replies
2
Views
1K
B Optimizing permutations of hero traits in a computer game
    • General Math
Replies
2
Views
716
B How to pick some numbers out of 13 integers, by a 4 digits code
    • General Math
Replies
4
Views
347
B How are permutations and probability related?
    • General Math
Replies
1
Views
1K
Insights Reduction of Order For Recursions
    • General Math
Replies
4
Views
2K
I How to find the nth binary permutation?
    • General Math
Replies
2
Views
2K
Mastering Combinatorics: Exploring the Formula for Permutations
    • Calculus and Beyond Homework Help
Replies
1
Views
624
Not a trained mathematician, but this seems to work consistently
    • General Math
Replies
9
Views
1K

Hot Threads

Recent Insights

Back
Top