For questions related to permutations, which can be viewed as re-ordering a collection of objects.

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4
votes
1answer
32 views

Proof of stars and bars formula

I am trying to prove a formula (for ways of distributing n identical balls among r persons when each person may get any number of balls) C(n+r-1, r-1). But I am not able to prove it. I may be doing ...
1
vote
0answers
63 views

Polynomial Interpolation When part of $y_i$'s are Shuffled

Hypothesis: Let $\vec{x}=[x_1,...,x_n]$ be elements of field $\mathbb{Z}_p$, where $p$ is a large prime. $x_i \neq x_j$, $x_i \in \mathbb{Z}_p$. Note $x_i$ values are NOT picked uniformly random and ...
-1
votes
3answers
23 views

how many ways a captain be chosen? [on hold]

from a group of $40$ players a cricket team of $11$ players is choosen. Then one of the $11$ is choosen as the captain of the team. How many ways this can be done ?
0
votes
2answers
380 views

How Can I calculate number of combinations/permutations with certain rules

Lets say I have 4 balls and when each ball is drawn it can be any value between 1-40 inclusive. If order isn't important then it would just be $40\cdot 39\cdot 38\cdot 37/4!$ But what if ball 1 had ...
0
votes
1answer
31 views

Finding all homomorphisms [duplicate]

How can I solve this question Find all group homomorphisms from $\mathbb{Z_{5}}$ into $\mathbb{Z_{12}^{x}}$?
0
votes
1answer
22 views

In how many ways that the letters of ENTERTAINMENT are arranged in a row where two Es are together and one is apart [on hold]

In how many ways that the letters of ENTERTAINMENT are arranged in a row where two Es are together and one is apart??
4
votes
1answer
35 views

Showing a subset of $S_n$ is a subgroup

Let $P$ be the set of all the elements of $S_n$ which can be written as $\sigma\mu\sigma^{-1}\mu^{-1}$ for $\sigma, \mu \in S_n$. Show this is a subgroup. This doesnt seem to be as simple as ...
0
votes
0answers
29 views

How can I formed as below permutation problem

Hi I am writing a program and i encouraged the below permutation problem and need your help. There are 4 boxes: 3 of them have 2 balls The one box has 1 balls. The question is what is the ...
2
votes
1answer
30 views

count permutations that do not contain repeated combinations

I am trying to count the number of permutations that do not contain order specific groupings that have occurred in permutations that have already been counted. Example: For the set {A B C D E}; if ...
5
votes
2answers
824 views

Find the center of the symmetry group Sn.

Find the center of the symmetry group $S_n$. Attempt: By definition, the center is $Z(S_n) = \{ a \in S_n : ag = ga \forall\ g \in S_n\}$. Then we know the identity $e$ is in $S_n$ since there is ...
1
vote
0answers
15 views

Number of injective maps from one finite set to another [duplicate]

$m\le n$ be natural numbers. What is the number of injective maps from a set of cardinality $m$ to a set of cardinality $n$ $?$ I think it is the number of ways $m$ ...
2
votes
1answer
746 views

Rearranging Equations with Factorials?

Hullo! This is my first time using this site. I have just begun tutoring a Math 12 student and I'm a little rusty on factorials. The stuff I'm stuck on is why : n!/(n-2)! = n(n-1). I seem to be ...
-1
votes
1answer
17 views

Random Permutation Polynomial With Fixed Inputs

Assume we pick uniformly random a permutation polynomial, $T$, of degree one. we define all polynomials over $\mathbb{Z}_P$. We have fixed inputs $x_i$ (e.g. $x_i \in [1,100]$) My Question: Is ...
0
votes
0answers
26 views

Calculating Combinations / Permutations [on hold]

How do I calculate the number of outcomes as a whole of a series of individual tests with there own outcomes? For example, the best description I could think of would be: There are 10 tests and each ...
0
votes
1answer
16 views

Proving that an adjacency transposition is the product of odd number of adjacencies.

A transposition in $S_n$ of the form $(i \ i + 1)$ is called an adjacency. I am trying to prove that, Given $i ∈ \{1, . . . , n − 1\}$, if $i < j$, the transposition $(i \ j)$ is a product of an ...
1
vote
0answers
39 views

I need the paper “ J. Zhang, A note on finite groups satisfying the permutizer condition, Sci. Bull. 31 (1986) 363–365” [on hold]

I need this paper " J. Zhang, A note on finite groups satisfying the permutizer condition, Sci. Bull. 31 (1986) 363–365", But i not found. Who can help me to find this paper ?
-8
votes
0answers
47 views

identity permutations [on hold]

I need some help with the following question : For the permuation $ π $ on n elements we define the term : $ π^k=i $ if the composition of π on it self k times is the identity permutation . (where ...
3
votes
2answers
4k views

Finding the order of permutations in $S_8$

Consider the group $S_8$. What is the order of $\sigma = (4,5)(2,3,7)$ and $\tau = (1,4)(3,5,7,8)$? My book says I should just use a trick by the order of a permutation expressed as a product of ...
-5
votes
0answers
24 views

how many transpositions exist in this permutation? [on hold]

For permutation \begin{pmatrix}1&...&l&l+1&...& l+k\\k+1 & ...&k+l&1&...&k\end{pmatrix}. The answer is kl. Thanks
2
votes
1answer
22 views

Reason of dividing to n! ( repetition ) on Permutations with Repetitions

I'm trying to figure out the reason of diving the number of permutations by the number of repetitions (in factorial). Shouldn't it be without the factorial? I don't get why are there is a factorial in ...
1
vote
0answers
39 views

How to find the number of solution of $x^n=1$ in the group $S_n$?

Suppose that $S_n$, the symmetric group of order $n!$ is given and for given $m\in \mathbb N$ fixed, we are to find the number of solutions to $\theta^m=e, \theta\in S_n$. Can someone tell me or give ...
-2
votes
0answers
63 views

the identity permutation [on hold]

for the permuation $ \pi $ on n elements we define the term : $ \pi^k=i $ if the composition of $ \pi $ on it self k times is the identity permutation . A. let $ a_n $ be the number of permutation of ...
2
votes
1answer
33 views

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: ...
5
votes
1answer
88 views

How many 4 digit number can be formed by 0,1,2,3,4,5 divisible by 4

How many 4 digit number can be formed by 0,1,2,3,4,5 divisible by 4 with repeatition My Approach: Last two digits can be 00,04,12,20,24,32,40,44,52 that is 9 possibilities for last two digits. ...
2
votes
2answers
33 views

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 ...
1
vote
2answers
21 views

If abc is a three digit number such that not one number is similar to other than how many possible values of ( a + 4b + c ) will be divisible by 40?

If abc is a three digit number such that not one number is similar to other than 1 How many possible values of ( a + 4b + c ) will be divisible by 40? 2 How many possible values will be ...
2
votes
3answers
123 views

Is there any good software that solves equations of permutation group elements?

I need to solve equations of permutation group elements (elements of $S_n$) that may not may not have solutions. The number of equations generally exceeds the number of variables. Is there any good ...
1
vote
2answers
403 views

ln how manyways can we distribute $7$ apples and $6$ oranges among $4$ children so that each child gets at least one apple.

In how many ways can we distribute $7$ apples and $6$ oranges among $4$ children so that each child gets at least one apple? I think this can be solved by using permutations because the word ...
5
votes
2answers
66 views

Average length of a cycle in a n-permutation

What is the average length of a cycle in a permutation of $\{1,2,3,\dots ,n\}$?
0
votes
0answers
25 views

Permutations of given length

Given the counts of each of three letters a, b, and c. I want to find all permutations of a given length where each letter can occur at most times as the given count. I am only interested in the ...
1
vote
1answer
1k views

what is maximum number of points of intersection between the diagonals of a convex octgon?

What is the maximum number of points of intersection between the diagonals of a convex octagon (8-vertex planar polygon)? Note that a polygon is said to be convex if the line segment joining any two ...
0
votes
1answer
36 views

How many 3 digit no.s can be formed so that the sum of two digits will be equal to the third digit?

Qn How many 3 digit no.s can be formed so that the sum of two digits will be equal to the third digit? Q I am confused in this question whether to take first 2 digits sum or any digit sum such ...
4
votes
3answers
65 views

How many 3 digit numbers can be formed using digits 1,2,3,4 and 5 such that the number is divisible by 6

How many $3$ digit numbers can be formed using digits $1,2,3,4$ and $5$ without repetition such that the number is divisible by $6$ First Approach: A number is divisible by $6$ if it is ...
0
votes
2answers
27 views

How many combinations are possible, if fare is 50 paisa?

Sherlock Holmes and Dr Watson travel from X to Y via metro. They have enough coins of 1,5,10,25 paisa. Sherlock Holmes agrees to pay for Dr Watson only if he tells all possible combinations ...
0
votes
1answer
55 views

Permutations excluding repeated characters

I'm working on a Free Code Camp problem - http://www.freecodecamp.com/challenges/bonfire-no-repeats-please The problem description is as follows - Return the number of total permutations of the ...
0
votes
2answers
37 views

Combination lock with continuous attempts

The lock has 4 symbols (A,B,C,D) and the password is 3 symbols long. Now, the lock does not "rest" after each attempt. So if I enter "ABCD" and the password is "ABC" or "BCD", it would open. I tried ...
0
votes
1answer
49 views

How many different words can be formed using the letters of the word “ PERMUTACION”?

Is there any guide to solve this? Edit: This is what I do. I used the permutations. Please check if I did the right thing? Since 11 words so i did 11Pr 1 letter 11p1 2 letter 11p2 11 3 letter ...
-2
votes
0answers
21 views

In a special deck of playing card, one which doesnt contain any Jack, Queen or King [closed]

Determine the probability of the following events: a. Drawing a space (one card) b. Drawing a black card (one card) c. Drawing of four hearts ( four card) d. Drawing of full house (five cards) e. ...
6
votes
2answers
872 views

Find the sum of all the number formed by 2,4,6, and 8 without repetition.Number may be of any digit like 2, 24, 684, 4862.

Find the sum of all the number formed by 2,4,6, and 8 without repetition.Number may be of any digit like 2, 24, 684, 4862. My Approach: single digit no formed = 2,4,6,8 sum= 2+4+6+8= 20 two ...
1
vote
2answers
1k views

Combinatorics-permutations and combinations

In a soccer tournament of 15 teams, the top three teams are awarded gold, silver, and bronze cups, and the last three teams are dropped to a lower league. We regard two outcomes of the tournament as ...
1
vote
3answers
62 views

How many ways can 6 cars ( 3 pink, 2 orange and 1 yellow) be parked in 6 parking slots in a row?

a. If the pink cars must be park together? - my answer is 4!3! or 144 b. If the orange cars must not be parked together? c. If you can't park the yellow on either end? d. If a pink car must be on ...
4
votes
3answers
50 views

Let $g_{n}$ be the no. of derangements with $n$ elements and $f_{n}$ the no. of permutations with one fixed point. Show that $|g_{n}-f_{n}|=1$

This is a problem from Loren Larson's "Problem solving through problems", 2.5.13, page 78. Let $S_{n}=${$1,2,...,n$}. A derangement of $S_{n}$ is a permutation with no fixed points. Let $g_{n}$ be ...
8
votes
2answers
144 views

Integer solution $(x,y,z)$ to $xyz=24$

Find the total number of integer solutions $(x,y,z)\in\mathbb{Z}$ of the equation $xyz=24$. I have tried $xyz = 2^3 \cdot 3$ My Process: Factor $x$, $y$, and $z$ as $$ \begin{cases} x = 2^{x_1} ...
0
votes
3answers
37 views

Axioms for Group Action

Reading the Wikipedia article on group action, I am wondering, why are the axioms stipulating that a group action obey both "compatibility" and "identity"? If a group action is merely a group ...
-2
votes
2answers
76 views

In how many ways can 4 red, 3 blue and 2 green balls be arranged? [closed]

In how many unique ways can 4 red, 3 blue and 2 green balls be arranged if they are indistinguishable aside from color?
0
votes
1answer
37 views

How do I find the number of solutions of the equation $r_1 + r_2 + … + r_k = n$

I was studying the multinomial theorem: $(u_1+u_1+...u_k)^n=\sum\limits_{r_1+r_2+...r_k=n}\dfrac{n!}{r_1!r_2!...r_k!}u_1^{r_1}u_2^{r_2}...u_k^{r_k}$ and my book said that the number of terms in the ...
1
vote
2answers
78 views

How many two letter words can be formed from 26 English letters?

There are 26 English letters(a-z). From layman approach, How can one calculate the possible two letter words from these 26 English letters?
2
votes
2answers
47 views

Determining the minimum dimension required for embedding a finite group

Consider the groups $S_3$ and $S_4$ which are the symmetric groups on 3 and 4 elements respectively. We note that $S_3$ can be realized geometrically as the set of all rotations and reflections of a ...
0
votes
1answer
53 views

How many 3-digit positive integers can be formed using the digit 0,1,2,3,4 and 5?

No repetition of digits? With repetition? If the integer must be greater than 400? (no repetition) If the integer must be even? If the integer must be odd? If the integer must be divisible by 5? (no ...