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
3
votes
1 answer

Equation on permutations

In a group of permutations of $n$ elements, there are two permutations $P_1$ and $P_2$ such that $P_2=P_1^e$. $P_1$ and $P_2$ have the same order $o$: $P_1^o = P_2^o$. How can I find $e$? $n$, $P_1, P_2$ and $o$ are known, $e$ is not known. Problem…
user6823
3
votes
0 answers

Find number of numbers which have the property that for each digit,not more than two digits smaller than that digit appear to the right of that digit

Consider all the $6$ digit numbers that can be formed using the digits $1,2,3,4,5$ and $6$,each digit being used exactly once. Find number of such six digit numbers which have the property that for each digit,not more than two digits smaller than…
Maverick
  • 9,172
  • 2
  • 30
  • 61
3
votes
1 answer

How many different numbers from $1,2,7,8$ taking one,two,three and four digits no repetitions and how many of them are above $200$?

Taking one, two, three and four digits from digits $1,2,7$ and $8$, and if repetitions are not allowed How many different numbers can be arranged? How many of them would be greater than $200$? I got the first answer $= 64$: $4$ one digit…
HN17
  • 195
3
votes
5 answers

$n$ balls numbered from $1$ to $n$

If we consider a box containing $n$ balls numbered from $1$ to $n$. If $455$ is the number of ways to get three balls from the box such that no two balls are consecutively numbered, then we have to find the value of $n$. Someone please help me…
Koolman
  • 2,898
3
votes
4 answers

Arrange 'ARRANGED' s.t. A and N aren't next to each other

I was looking at a solution for a question regarding permutations at this thread Arranging letters with two letters not next to each other and I thought of another question. In how many ways can the word ARRANGED be arranged if A and N aren't next…
Kong
  • 884
3
votes
2 answers

How many paths possible in this grid given this specific conditions?

In a grid, There is a bottom-left point i, with co-ordinate (0,0) and top-right point j with co-ordinate (10,10). A person is standing at point i, He can go up (1 unit), right (1 unit) and diagonally (1 unit diagonally) given that person don't cross…
user1509863
  • 33
3
votes
1 answer

About circular permutation

I know this is a physics group, but then I think you guys can answer me .. anyone can explain how circular permutation work? From the explanation from the book, it is understood that if CW $\ne$ ACW , it is $(n-1)!$. if CW $=$ ACW, $(n-1)!/2$ . . .…
Delta
  • 39
3
votes
3 answers

How to express/write a permutation of a Set?

How to express a permutation (without repetition) of a Set $A$? I'd like to create a set $P$ of tuples while equal tuples should only occur once in the set $P$. Tuples are equal when e.g. $\{a, b\} = \{b, a\}$. Tuples of the same values should not…
Thomas
  • 191
3
votes
1 answer

Circular permutation - Arranging 4 persons around a circular table where 8 seats are there.

Suppose 4 persons $A,B,C$ and $D$ sit around a round table with 8 seats. Rotation by 8,16,24,... seats defines same arrangement and other rotations gives different arrangements. Find the number of ways that these four people can be seated at the…
Kiran
  • 4,198
3
votes
2 answers

Permutations with conditions - small exclusions from a finite pool

I am trying to calculate the number of possible set-ups for a game. There are 4 colors of beads (red, blue, green, and clear) and 18 places the beads can be placed. Using 5 beads of each color, you have 4×(18!/3!5!5!5!)+6×(18!/4!4!5!5!) (Roughly 7…
rob
  • 45
3
votes
1 answer

In how many ways can five-digit numbers be formed by using digits $0,2,4,6,8$ such that the numbers are divisible by $8$?

In how many ways can five-digit numbers be formed by using digits $0,2,4,6,8$ such that the numbers are divisible by $8$? Assume the case in which repetition is not allowed Our Approach: Case1: When repetition is not allowed. We start to make…
justin takro
  • 1,288
3
votes
2 answers

Permuation and Combination: Selecting n numbers such that such that sum is less than m

The value of n can be 0,1,2,3....and so on For example If we have to select 2 numbers such that the sum of all them can be less than 2 Manually the combinations can be (0,0), (0,1), (1,0), (2,0), (0,2) and (1,1) So there are 6 ways How do we solve…
Sanchit Kapoor
  • 131
3
votes
1 answer

square of a permutation cycle

$$\sigma = \begin{bmatrix} 1 &2 &3 &4 &5 &6 &7 &8 &9 \\ 1&5 &7 &4 &6 &9 &3 &2 &8 \end{bmatrix}$$ $$\sigma^{2} = \begin{bmatrix} 1 &2 &3 &4 &5 &6 &7 &8 &9 \\ 1& 6&3 &4 &9 &8 &7 &5 & 2 \end{bmatrix}$$ Given $$\sigma$$…
delta
  • 33
3
votes
1 answer

The number of adjacent transpositions

If $\alpha\in S_{k+l}$, $\alpha=\left(\begin{array}{cccccc}1&\cdots&k&k+1&\cdots&k+l\\l+1&\cdots&l+k&1&\cdots&l\end{array}\right)$, for $k,l\in\mathbb{Z}^+$ then how can I express $\alpha$ as the composition of adjacent transpositions? Indeed I…
kurtzdoni
  • 600
3
votes
1 answer

How many permutations will there be to this problem?

How many permutations of the following pattern will there be. The order has to stay the same. In other words, you can only swap the 'B' with another 'B' because it will not affect the pattern? B C B C C B A B C A C My guess is there are 5760…
Desmond Oliver
  • 31
1 2 3
…
69 70