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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In how many $3$ letters word can be arranged from the word 'MOVIES'?

In how many $3$ letters word can be arranged from the word 'MOVIES'? my answer is $^6P_3=120$ is the answer correct?
Sakthi Seelen
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How many 4 digit numbers can be formed using numbers 2,3,4,5,6,7 such that the number is only once divisible by 25?

Q How many 4 digit numbers can be formed using numbers 2,3,4,5,6,7 such that the number is only once divisible by 25? My approach: Case1: Unit digit is 5.Ten's digit will be 2 or 7.Taking here 2 first No of ways=4*3*1*1=12 Case2: Unit digit is…
justin takro
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Permutation & Combinations - Distribution

The number of ways in which n distinct things can be distributed among n people so that at least one person does not get anything is 232. Find n. I think every object has (n-1) option. So (n-1)^n=232. But this gives the answer as 4.4(not a whole…
Shashank Gupta
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In how many words the letter of word RAINBOW be arranged so that only 2 vowels always remain together?

My Approach: RAINBOW has 4 Consonants and 3 vowels. Out of 3Vowels 2 vowel are selected and arranged in 3P2 ways and the rest letters are arranged in 5! ways(1vowel and 2 consonants) The Required arrangement is: 3P2*5!=720 But the Ans is…
Jack
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Clarification of a concept in Permutation

Statement 1 No. of ways in which $(m+n+p)!$ different things can be divivded into different groups containing m,n & p things respectively. is $(m+n+p)!/m!n!p!$ Statement 2 If $m=n=p$ and the groups have identical qualititive characteristic then the…
user237454
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Permutations of {1, 2 .. 30} where $a_n - a_n-m$ is divisible by m from {2, 3, 5}

There are $N$ permutations $(a_1,a_2,\dots,a_{30})$ of $1,2,\dots,30$ such that for $m\in\{2,3,5\}$, $m$ divides $a_{n+m}-a_n$ for all integers $n$ with $1\leq n
abcd8642
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how to solve this permutation

In how many ways a Table with $N$ rows and $M$ columns can be created so that sum of elements in $i$th row is greater or equal to the sum of elements in $(i-1)$th row for $ 2 \le i\le N$ and sum of elements in $N$th row is less or equal to $M$. Each…
user2399614
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A combinatorial question about outer automorphisms of $S_6$

Quite possibly I'll solve this and post my answer below, but maybe others will post better answers before I get to that. Or after.$^\dagger$ The group of permuations of $\{a,b,c,d,e,f\}$ is generated by $15$ elements of order $2$, each of which is…
Michael Hardy
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Is the sequence generated by two permutations periodic?

It's quite easy to prove that given an application: $\sigma:[1,n]\to [1,n]$ we know that the sequence: $$Id_n,\sigma,\sigma^2,\sigma^3,\cdots,\sigma^m,\cdots $$ Is periodic after some index $k\leq n^n$ Now my question is Given two applications…
Elaqqad
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How many inversions in a permutation?

For the permutation $\begin{pmatrix}5&2&4&3&6&1\\4&1&3&2&6&5\end{pmatrix}$, determine if it is even based on its inversions. So here's my trouble; I've worked out the inversions for the top row as $(5,2),(5,4),(5,3),(5,1),(2,1),(4,3),(4,1),(6,1)$…
marquis
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Number of ways in which $38808$ can be expressed as a product of 2 coprime factors?

Number of ways in which $38808$ can be expressed as a product of $2$ coprime factors ? the answer given is $8$ ways, what I did was, $$38808 = 2^3 \times 3^2 \times 7^2 \times 11$$ so the number of ways of expressing $38808$ as product of $2$…
Tomarinator
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Permutations on a set with certain conditions.

Suppose we have a set $S=\{1,2,3,x,y\}$. There are $5!$ ways to rearrange the elements in the set, but I am confused about how to find the number of ways to rearrange the set given that $3$ comes before $2$ which comes before $1$ (or something like…
FinneganJ
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How to calculate total results of combinations of letters

I am programmer and have developed an algorithm to run a processor intensive function on all the permutations of 2 letters (X and O) when we define how many X's and O's there will be. For example, I may run F(10, 5) which would run all the…
mrkmg
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Illegal permutations give a nonzero answer

I am told that a random variable can take a value of $+1$ or $-1$. I am given the total number of times the random variable is counted, $N$, and the sum of the random variables, $n$, and asked to find how many ways such an outcome is possible. So if…
Dargscisyhp
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4 People Gift Exchange

4 people are exchanging gifts. How many combinations are there so that no one receives their own gift? I tried this problem myself, and got 3!. My friends told me that it's 9. I got 3! because I thought: Person A: Has 3 options for gifts (excluding…
Jon
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