Mathematics Stack Exchange
Mathematics Stack Exchange

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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Is the Wikipedia Explanation of Cyclic Permutations Incorrect (As checked on the 2nd Oct 2015)

At the very beginning of the cyclic permutation Wikipedia article. There is a brief example of a cyclic permutation vs a non-cyclic permutation. The article says that: $\lbrace1,2,3,4 \rbrace \rightarrow \lbrace 3,4,2,1 \rbrace$ is cyclic,…
user15766
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The number of ways of arranging these guest having $16$ guest have to be seated around $2$ circular tables with following conditions

$16$ guest have to be seated around $2$ circular tables,each accommodating 8members.$3$ particular guest desire to sit at one particular table and $4$ others at the other table.The number of ways of arranging these guest is: options a) $9C5$ b)…
Jack
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In how many ways can one or more of $5$ letters be posted into $4$ mail boxes, if any letter can be posted into any of the boxes?

In how many ways can one or more of $5$ letters be posted into $4$ mail boxes,if any letter can be posted into any of the boxes? Options: a) $5^4$ b) $5^4-1$ c) $5^5-1$ d) $4^5-1$ My Approach: A person goes to post his letter in the mail box he…
Jack
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Arranging letters with two letters not next to each other

just wanna know what's the answer to this one. How many ways can the word "ARRANGED" be arranged so that N and D aren't next to each other? Thanks. :)
subwoah
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In how many ways can the elements be divided into 2 groups given A set "a" having 6 elements?

A set "a" has 6 elements.In how many ways can the elements be divided into 2 groups? Options given: 1) $62$ 2) $31$ 3) $52$ 4) $32$ My Approach: I divided the items into 2 unequal groups of 4 and 2,5 and 1,6 and 0,3 and 3. I get $6!$/$2!$ .…
justin takro
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The total number of ways in which six “+” and four ”-“ signs be arranged so that no two “-“ signs occur together is?

The total number of ways in which six “+” and four ”-“ signs be arranged so that no two “-“ signs occur together is ?
Vignesh Amin
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Permutations and maps

Let $X,Y$ be sets and let $f\colon X\rightarrow Y$ be an invertible map. We let $f^{−1}\colon Y\rightarrow X$ denote the inverse map of $f$. For any permutation $\pi \in {\rm Perm}(X)$ of $X$ , define the map $\sigma\circ\pi\colon Y\rightarrow Y$ as…
user271716
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How many permutations of a deck of cards where suit doesn't matter

Starting with a standard $52$ deck of cards how many ways can you order all $52$ cards. But for this, the actual suits don't matter. So if you have a particular order, then you switch the position of the $2$ of clubs with the $2$ of hearts, that is…
Socko
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How would I solve this theatre-related permutations problem?

A theatre company is casting seven roles for a play that has four males and three females. If 10 men and 8 women audition, how many ways can the director cast the play? (the roles are all different)? This problem has given me trouble because i'm…
Mark Gregg
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6-team Round Robin

Is it possible to create a schedule where we have 6 teams play 5 different games with each team playing each game and each team only once? Or do we have to increase the amount of games to make this possible? The amount of teams cannot change,…
MattShuey
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Permutations with 26 letters

Not totally sure if I'm understanding the questions correctly: Consider the permutations of the set of 26 letters of the English alphabet How many total permutations are possible? P(26,26)=26! How many permutations begin with a? P(26,25) How many…
ematth7
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Permutations of sets within larger sets

I am trying to find a formula to give me the number of permutations of 3 numbers across multiple sets of numbers. For example I have 5 different sets call them a,b,c,d,e with numbers 1-10 and I want to know if we use one number from each how many…
Gordon
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How many combinations are possible, if fare is 50 paisa?

Sherlock Holmes and Dr Watson travel from X to Y via metro. They have enough coins of 1,5,10,25 paisa. Sherlock Holmes agrees to pay for Dr Watson only if he tells all possible combinations of coins that can be used to pay for the ticket. Q1 How…
justin takro
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finding out numbers in rows and columns

If $2731$ has to appear in $x$, we should have $910$ in $V$ If $2731$ has to appear in $y$, we should have $546$ in $V$ If $2731$ has to appear in $z$, we should have $390$ in $V$ I am stuck with this. How to find out whether $910,546,390$ are…
Hari
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Limiting how often an element can repeat

Say I have two elements (0, 1) and I want to find the number of permutations of sequences of, say, length 10. However, I want to limit it so that "1" can never appear more than twice in a row, with no limits on "0." So, 0110110110 is ok, but…
Jake Malloy
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