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.

12854 questions
2
votes
1 answer

Permutations starting with a specific letter

Ok, this is a homework question and I think I've resolved it but I want to bounce it off you guys. I have a $6$ letter word with no repeated letters. I need to calculate how many $3$ letter words can be formed from this word and all must start with…
Moira
  • 41
2
votes
2 answers

$5$ chem students, $6$ maths students and $7$ physics students permutation

$5$ chem students, $6$ maths students and $7$ physics students. Find the number of arrangements if a)Chem majors are to occupy the first 5 positions b)Chem majors cannot occupy the first 5 positions c)Students with the same major must be together in…
RStyle
  • 607
2
votes
2 answers

Suppose $π ∈ S_n$, and for this $π$ define $C_π : S_n → S_n$ be defined by $C_π(σ) = πσ$. Why is $C_π$ a bijection?

$S_n$ is the set of all permutations. I'm just starting on this material, so I'm confused on how to read this problem. Does the function consist of multiple permutations (i.e. the permutation of a permutation)? A property of a permutation of $\{1,…
Chris
  • 1,129
  • 1
  • 9
  • 18
2
votes
2 answers

How many 20 digit numbers have 10 even and 10 odd digits?

How can I perform operations so as to get this value? Number should not have leading zeros.
user249117
  • 245
2
votes
3 answers

Counting - Permutations & Combinations

Two series of a question booklet for an aptitude test are to be given to twelve students. In how many ways can the students be placed in two rows of six each so that there should be no identical series side by side and that the students sitting one…
Bulbuul Dev
  • 89
2
votes
6 answers

Permutation seating arrangment 5!.3!

What wold be the answer for this How many ways can 3 boys and 4 girls sit in a row if all the boys are sit together. Answer listed as $5!\cdot3$! $4+3 = 7$ what is 5 doing here? someone please break the steps of solving this? what does mean by…
user1419170
  • 305
2
votes
3 answers

Find the number of distinct integers with non-decreasing digits formed from one or more of the digits $2, 2, 3, 3, 4, 5, 5, 5, 6, 7$

Suppose integers are formed by taking one or more digits from the following: $2, 2, 3, 3, 4, 5, 5, 5, 6, 7$. For example, $355$ is a possible choice while $44$ is not. Find the number of distinct integers that can be formed in which the digits are…
user44689
  • 47
2
votes
3 answers

Permutations and arrangements of toy animals

The question is: A baby has nine different toy animals. Five of them are red and four of them are blue. She arranges them in a line so that the colours are arranged symmetrically. How many different arrangements are possible? I understand that…
CCC
  • 1,031
2
votes
1 answer

Permutations with restrcitions

I have n distinct numbers , so I will have n! permutations. Now I want to insert another number into this set , and find the total number of new permutations. But there are some restrictions. This new number cannot be placed adjacent to k numbers in…
user253651
  • 237
2
votes
2 answers

Similarity between two nPn permutations of the same set.

Given two $nPn$ permutations of the same $n$-sized set, how can one find out the similarity between these permutations over the interval $[0, 1]$?
user1030497
  • 53
2
votes
4 answers

How many possible outcomes are there when 5 similar dices are rolled?

In this question If I consider first total no of outcomes as $6^5$ , then I divided it be ${6\choose5} *5!$ since there are 5 similar dices so the outcome (1 2 3 4 5 ) will be similar to (5 4 3 2 1) . Now what's wrong with this approach ?
radhika
  • 361
2
votes
1 answer

subgroup generated by a permutation

For instance, if I take the permutation $\alpha=(123)(67)(458) \in S_{10}$, what is the subgroup generated by it? Knowing that the order of $\alpha$ is 6, I already calculated $\alpha ^0, \alpha ^1$ and so on, until $\alpha ^5$. How do I proceed…
Encontro Regional Sul
  • 47
2
votes
2 answers

Sum on the ratio of elements in a set and its permuation

lxhfcjksdnbcjk s dkjbdjksehdkin swdwskdnbwsdkjwsnbdkwnsknw
Jason Burt
  • 45
2
votes
1 answer

Arranging cards so that no two consecutive values remain consecutive

Let us say we have 52 cards with values ranging from 1-13 (4 sets of cards from 1-13). Assume that you wanted no two consecutive values to be next to each other in the pile of cards. For example, a 3 cannot be next to a 2 or a 4. How many ways can…
Jaywalker
  • 175
2
votes
1 answer

How many possible passwords are there with these restrictions?

Assume that a legal password is $10$ characters long, using the following $3$ types of symbols: $26$ alphabets, $10$ digits and $6$ special characters (such as ! and *). In addition, it must use at least $2$ of these types of symbols. How many legal…
user88528
1 2 3
…
69 70