Questions tagged [permutations]

For questions related to permutations, which can be viewed as re-ordering a collection of objects.

The word permutation has several possible meanings, based on context. In combinatorics, a permutation is generally taken to be a sequence containing every element from a finite set exactly once. Permutations of a finite set can be thought of as exactly the ways in which the elements of the set can be ordered.

In group theory, a permutation of a (not necessarily finite) set $S$ is a bijection $\sigma : S \to S$. The set of all permutations of $S$ forms a group under composition, called the symmetric group on $S$.

Reference: Permutation.

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What is a permutation reordering?

What is a permutation reordering? Example Problem Input: A sequence of $n$ numbers: $a_1,a_2,\dotsc,a_n$. Output: A permutation reordering $(a_1',a_2',\dotsc,a_n')$ of the input sequence such as $a_1'
techno
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What's an effective way of comparing orderings?

Given two orderings of some set of things, what's an effective way to quantify how similar the orderings are? For instance, say I have the orderings 1 2 3 4 5 2 3 4 5 1 If I just use the number of elements in the right positions, I get that the two…
David Faux
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Permutation of natural numbers

Find the number of permutation of {1,2,3,4,5,6} such that the patterns 13 and 246 do not appear. Show the steps .
U-571
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Permutation and combination of letters

I need help with the following question: "Given that a computer can only type letters A,B,C,D and E, how many ways can I type in 6 letters such that they must contain at least all of the different letters? ie. AABCDE ABCDEA ABCDEB" My professor…
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probability and combinations with the word REGULATIONS

If the letters of the word REGULATIONS are arranged at random,what is the probability that there will be exactly 4 letters between R and E? The answer in my book is given as 11!/(9C4 x 4! x6!x2!) .Shouldn't the answer be upside down because…
ayush
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Permutation question: Pick out 2 items from 4 items which 2 duplicated, is there any formula?

If given ABBC, find the permutations if 2 letters are picked. If I calculate manually, they are: AB, AC, BA, BB, BC, CA, CB, 7 permutations. Is there any formula to solve this type of question? (Meaning, picking r number of letters from n number of…
Allen
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Possible variations in a bilateral symmetric system

Can someone shed a light on how to solve something like this? I've been looking for permutations but so far I found it very confusing. As I'm not at home atm, I can't reach for my math books either for an answer. Maybe you can help? Given: a 5x5…
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How many possibilities in tinyurl

Looking at tinyurl, there is anywhere from 1 digit to 7 digits of I believe 36 choices (lowercase letters a to z and digits 0 to 9) How do I calculate mathmatically the number of permutations of the string with 1 to 7 digits and 36…
Dean Hiller
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What is the total number of permutations of n digits where all digits will exchange their positions?

As we know, Total number of permutations of the digits 12345 is 5!. Well, I am looking for another interesting fact. How many permutations among them are in the way that no digit is in its original position? (For example, 54231 is one of such ones,…
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How Can I calculate number of combinations/permutations with certain rules

Lets say I have 4 balls and when each ball is drawn it can be any value between 1-40 inclusive. If order isn't important then it would just be $40\cdot 39\cdot 38\cdot 37/4!$ But what if ball 1 had to be between 2 and 9, ball 2 between 9 and 20 and…
Gab
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Permutations with prior positions

In how many ways $P,Q,R,S,T,U$ can be arranged such that $ P, Q$ should come before $T,U$ ? Do we have to find the ways that $P$ and $Q$ can be placed in the first four position?
user2378
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Count of 3-digit numbers

How many different three digit numbers can be formed with the digit $1,2,3,4,5,6,7,8$ none of the digit being repeated in any of the numbers so formed? $120/1200/180/270$ My attempt: $8*7*6=336$, but it's not an option. I wish somebody could help.
aarbee
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N people sit at a round table, starting from #1, every other one leaves, who's the last one?

For example, there are 10 people sitting there. So the 1st round, such people leave: $$\#1, \#3, \#5, \#7, \#9$$ and remains $$\#2, \#4, \#6, \#8, \#10$$ Then the 2nd round, such people leave: $$\#2, \#6, \#10$$ and remains $$\#4, \#8$$ Then the…
athos
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Permutations and Combinations Question?

Mr and Mrs Jones and 6 guests sit around the dinner table. In how many ways can they be arranged if the two host are separated? The answer says 3600, but I could never get that. My working out was 7! - 2!5! (total number of permutations minus the…
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Number of words which are created from 19 letters

There is a set of 19 characters A,B,C,. . . ,S. What is the maximum number of words of 16 characters that can be created from them if we require them to contain the character A is present once, character B is present twice, character C is present…