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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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Subgroup of $S_{2n}$ that sends evens to evens and odds to odds.

I got this question in the exam: $T_{2n}$ is the subgroup of $S_{2n}$ that sends even numbers to even numbers and odd numbers to odd numbers, for example: $(2 4 6 8)(1 3 5)$ is a permutation in $T_{2n}$. what is the index of $T_{2n}$ in $S_{2n}$…
hessssss
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The number of arrangements when twelve people sit in circle such that two certain people cannot be together

There are twelve people, arranged in a circle. Two people, for example, Mike and Ike, can not be together. This is what I have done: $$\frac{12!}{12}-\frac{11!2!}{12}$$ The first section representing the total arrangements in a circle, and the…
john2546
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How many permutations of $5$ characters with constraints...

Say I have characters abcde and the following constraints: a must come before b a must come before c c must come before d I thought the answer is $\frac{5!}{2!3!} = 10$. $2!$ comes from a$\to$b and $3!$ comes from a$\to$c$\to$d. However, if I…
user3912349
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Qualities of Even Permutation Groups

I need some help figuring out some qualities of even permutation groups. Consider $E_n$ to be a subset of the bijection set $S_n$ (bijections over $[n]$) that consists of all even permutations. I want to show that there are no trivial normal…
Jake
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Finding the number of objects in permutation

What is n in this permutation, P(n, 3) = 60? Please help me solve this.
Stephen Mark
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Permutation problem: create words from letters

I'm stuck on this problem: Consider the five letters A, B, C, D, and E. How many words with four letters can you create if each letter can be used at most two times? (One letter can i.e. be used 0, 1, or 2 times) At first I thought it would be…
user5744148
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count of distinct permutation of N elements when non of the given m pairs is a part of the permutation?

Suppose i am having a permutation of N items(from 1 to N) and M pairs,then what will be the no of different permutations under condition that any of M pairs should not come together? For ex - Suppose i have N = 5, So i have 1 2 3 4 5 Now for M =…
Simpi
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How many numbers with distinct digits are possible product of whose digits is 28?

This is a question asked in India's CAT exam: http://iimcat.blogspot.in/2013/08/number-theory-questions-and-solutions.html How many numbers with distinct digits are possible product of whose digits is 28? A. 6 B. 4 C. 8 D. 12 Firstly, I…
Nav
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How many ways to seat n people at a round table of size k when k is significantly larger than n?

According to a math website I'm looking at (http://web.eecs.utk.edu/~booth/311-04/notes/combinatorics.html), if you have a circular permutation situation (such as a round table), and there are e empty spaces, then the formula is... (n-1)! / e!…
user2779949
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Number of permutations 6 digits three numbers

I've lost my PIN that encrypts the hard drive of my laptop ! What I can recall narrows the permutations down to a number that would be worth a brute force attempt I think. It got me thinking, how does one calculate the permutations given the…
chrisjleu
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Permutation of few elements in a particular order

In a conference 10 speakers are present. $S(1)$ wants to speak before $S(2)$ and $S(2)$ wants to speak before $S(3)$, then the number of ways all the 10 speakers can give their speeches with the above restriction if the remaining speakers have no…
exilednick
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Determine the total number of $4$-digit numbers which can be obtained using the digits $1, 2, 3, 4, 5$.

It's a basic question, but I don't know why I am getting confused. Determine the total number of $4$-digit numbers which can be obtained using the digits $1, 2, 3, 4, 5$. Also find how many of them are divisible by $4$.
Paras Sidhu
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How many 4 digits numbers divisible by 5 can be formed with digits 0,1,2,3,4,5,6 and 6?

How many 4 digits numbers divisible by 5 can be formed with digits 0,1,2,3,4,5,6 and 6 options: a) $220$ b) $249$ c) $432$ d) $216$ MyApproach: To form a 4 digit number divisible by 5 using given numbers I make cases here: Unit Digit is $0$ and…
justin takro
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What is the sum of all such possible numbers given the following conditions?

What is the sum of all such possible numbers given the following conditions that A 4 digit number is formed using the digits 0,2,4,6,8 without repeating any one of them.? MyApproach: If you fix 8 as the last digit, you see that there are 3⋅3⋅2…
justin takro
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Permutation and fundamental principle of counting

how many numbers are there between 100 and 1000 such that at least one of their digits is 7?? I solved this question by making 3 cases(as 3 digit numbers are to be made) but i am not getting the right answer-- (the question says at least one 7 that…
Freelancer
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