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

Permutation Algorithms

Take a truly random binary string of say $64$ bits , all the ones and zeros are considered IID variables. Now perform the Fisher-Yates shuffle on this string to rearrange the bits. Are the bits still considered to be IID variables after shuffling?
William Hird
  • 41
-2
votes
4 answers

4 digit no. divisible by 5 permutation/combination

Using Permutations/ Combinations The question is: How many $4$ digits no. are divisible by $5$ if no $2$ digits are the same. The answer is: $952$ Thanks
Sam
  • 1
-2
votes
1 answer

Permutation of digits

Find the number of permutation of 6 digits from the set $\{1,2,3,4,5,6\}$ where each digit is to be used exactly once, so that the chosen permutation changes from increasing to decreasing or decreasing to increasing at most once e.g. the strings…
Maverick
  • 9,172
  • 2
  • 30
  • 61
-2
votes
1 answer

Simply showing the addition of permutations

How can I show for example AB+BC+AC simply. It is adding up the permutations of n numbers. Another example would be ABC+ABD+ACD+BCD. Sorry I'll try to make it clear with an example ( which is sort of the problem is know the terminology to use) If…
Boof
  • 3
-2
votes
1 answer

Numbers of words allowing repetition

10 different letters of an alphabet are given. words with 5 letters are formed from these given letters.I have to determine the number of words which have at least one letter repeated. Answer is - 69760 Can someone please help me solve this?
user6037890
  • 11
-2
votes
2 answers

Can you create a formula for the amount of possible permutations of a three digit number, who has a digit sum equal to 4

Can you create a formula for the amount of possible permutations of a three digit number, who has a digit sum equal to n?
user330409
-2
votes
3 answers

Value of factorial zero

The value of factorial zero is equal to one. I have understood the mathematical interpretation of factorial zero. But how can I explain the meaning of factorial zero in common language
Achari S Ganesha
  • 898
-2
votes
2 answers

Finding numbers which are composed of the digits 2 and 5

How many numbers are there between $100$ and $1000$ including $100$ such that every digit is either $2$ or $5$.
Nkd Nkd
  • 13
-2
votes
2 answers

Find The Number Of Permutation

I was solving one probability question, and to solve the problem I could relate it to binary and want solution. The question was that in a fair toss repeated 10 times, what's the probability of 10th try to be the 5'th head. I used brute-force and…
Kishan Kumar
  • 171
  • 1
  • 11
-2
votes
1 answer

Compute Square of Permutation

Dr. Pinter's "A Book of Abstract Algebra" presents the preface to a few exercises: In $S_{5}$, express each of the following as the square of a cycle (that is, express $\alpha^{2}$ where $\alpha$ is a cycle). I solved the first problem, $(132)$, by…
Kevin Meredith
  • 969
-3
votes
4 answers

How many numbers lying between 10 and 100 can be formed with the help of digits 1,3,5,7,9?

Please help me!! i don't know how resolve this problem. This is exercise from permutations in my school. hope you guys can help me :)
user56797
  • 17
-3
votes
1 answer

Permutations of word MANIFOLD

In how many ways can the letters of the word MANIFOLD be arranged so that the vowels are separated? I tried total permutations in which vowels are together, which gives 36000 which was wrong.
Techievent.in
  • 1
-3
votes
1 answer

In how many different ways can the letters of the word 'APTITUTE' be arranged so that all the vowels are in the beginning?

In how many different ways the letters of the word 'APTITUTE' can be arranged so that all the vowels always in beginning ? $48$ $72$ $576$ $2880$ $960$
drek
  • 1
-3
votes
2 answers

How many words can be formed from all the letters of the word 'INITIAL' that start and end with the letter 'I'?

How many words can be formed from all the letters of the word 'INITIAL' such that all words must have started and ended with letter 'I'?
drek
  • 1
-3
votes
3 answers

If the letter ATTRACTION was written in random, then find the number of ways with no two T's occurring together.

Here is the question: I JUST WANT TO KNOW THE MISTAKE IN MY METHOD: Here is how I solved but my answer is incorrect: the correct answer is (7!/2!) 8C3 Thankyou
Yb609
  • 95
1 2 3
…
69
70