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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How many different combinations are possible

Say there are 4 stations for ice cream toppings. station1: 3 choices station2: 2 choices station3: 2 choices station4: 3 choices How many different combinations toppings can I get assuming I pick 1 topping from each station? Would it be 3 * 2 * 2 *…
Lightsout
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Circular array with minimum absolute difference among adjacent elements

Given a circular array, rearrange the array so that the maximum absolute difference between adjacent elements among all elements is minimum. Can anyone help me with this?
leader
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Suppose we have a chair with $n$ legs and it stands with all legs irrespective of floor's quality i.e smoothness,evenness, then what is $n$?

Suppose we have a chair with $n$ legs and it stands with all legs irrespective of floor's quality i.e smoothness,evenness, then what is $n$? 1)2 2)3 3)4 4)5 I have no clue what they want to say, thank you for helping.
Myshkin
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Solving equation with permutations

I am trying to find the positive integer solutions to the following permutation equation: $$\phantom{.}^{n+1}P_{3}=4\phantom{.}^{n}P_{2}.$$ I'm really lost I don't know what I'm doing. I've try doing what I read off from other problem but I'm feel…
user146908
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Combination without repetition

There is a four digit code. Repetition of the same code is not allowed. How many possible combinations can be possible? I tried it as follows, As repetition of the same code is not allowed so it should be $10P4$ choices?
user2857
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Cyclic permutation with restriction, am i wrong?

there are 4 boys and 4 girls, how many ways they are arranged to sit in circular table if the 3 boys always together? i found someone's video and the answer is just 5!3!, there are 4 boys why he didn't choose 3 boys from 4 boys? let say the 4 boys…
cahya python
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Find $\alpha,\beta,\gamma\in S_4$ such that $\alpha\beta=\beta\alpha$, $\beta\gamma=\gamma\beta$ but $\alpha\gamma\neq\gamma\alpha$.

Can you give an example for $\alpha,\beta,\gamma\in S_4$ (permutation group for the set $\{1,2,3,4\}$) such that $\alpha\beta=\beta\alpha$, $\beta\gamma=\gamma\beta$ but $\alpha\gamma\neq\gamma\alpha$. I have tried many times but failed.
Stephen
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How many ways can word "ASSISA" arranged

This is a question from permutation, word "ASSISA" can be arranged in how many ways such that all 'S' are togather?
karthik_personal
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What does multiplication mean in the context of permutations?

I understand how to calculate permutations so: if I have 5 people: A,B,C,D,E how many ways can you sit them down if you have 3 chairs? Answer: 5*4*3. Also, I get that, for example, in my first chair I have 5 possible people that I can sit down,…
Felipe Araya
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Formation of words having length 5 by using 2 letters

In how many ways can 5 letter words be formed with 2 letters - Y and N. Ex - YYYNN, NNNYY etc.
New
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seating arrangments with n chairs but the first chair must be a girl

Take the example of 2 chairs: there are two possible arrangments as there must be a girl in the first chair, gb or gg The problem requires you to find the number of girls in all arrangments ie. for 2 chairs there are and for 3 chairs there are 8. I…
arvass
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I have 100 hundred different items. How to I calculate all possible combinations?

ELI5 the formula to figure out all possible combinations without repeating any items but no upper or lower limit of the number to include. Order does not matter.
jtgis
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Permutations of alike objects

If I have $1$ jar of $20$ balls with $10$ red, $5$ blue and $5$ yellow, $1$ jar of $30$ balls with $10$ red, $10$ blue and $10$ yellow and $1$ jar of $50$ balls with $15$ red, $20$ blue and $15$ yellow, but I can only pick three from each jar. How…
NAZBOL
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In how many ways can a king( as in chess ) move from one square to another diagonal square at the end of six moves?

I was able to solve a variant of this in which the king could not move diagonally, but I feel that the method I used for that is not the most efficient one. So, how do I approach this prob?
user585278
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Decide how many elements who commutate with this symmetric group?

Let $S_3$ be the symmetric group on $\lbrace 1,2,3\rbrace.$ Decide how many elements who commutate with $(23)$ Permutation naturally commutes itself, with it's inverse and with the identity permutation. So that's 3. And then I'm insecure. What…
soetirl13
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