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

learn more… | top users | synonyms

0
votes
1answer
20 views

Count no. Of ways

If $n$ identical balls put into $m$ identical boxes, how many ways it can be done, provided that boxes may be empty and all balls have to be put into these boxes at each time.
0
votes
1answer
19 views

Probability of item distribution with a restriction

I'm having a hard time analyzing my research data, and was wondering if anyone had any suggestions? I've reworded the question so it is presented more like a statistics problem. There are $x$ number ...
1
vote
2answers
33 views

Sum of Binomial Series of form $\binom{2000}{3k-1}$

Find the Value of $$ \binom{2000}{2}+\binom{2000}{5}+\binom{2000}{8}+\cdots+\binom{2000}{1997}+\binom{2000}{2000}$$
2
votes
2answers
48 views

(12345) is an even permutation of S_5. True or False?

The answer i had for this question was True, yet i'm not sure. Well, from what I know so far was that: $(12345)$ can be expressed as a number of 4 transpositions such as: $(12)(23)(34)(45)$ which is ...
0
votes
1answer
27 views

Conjugate subgroups of $S_4$

$A = \langle (1,2,3),(1,2)\rangle$ $B = \langle (1,2,4),(1,2)\rangle$ $C = \langle (1,3,4),(1,3)\rangle$ $D = \langle (2,3,4),(2,3)\rangle$ I want to proof that these subgroups of $S_4$ ( which ...
2
votes
3answers
77 views

How do I solve for n in this permutation question?

I have the following question: Solve for n: $$_nP_3 = 6_{n-1}P_2$$ I don't know how I should begin to tackle this problem? Any tips/help would be appreciated.
1
vote
2answers
34 views

Proof that $\det(A)=\det(A^T)$ using permutations.

I'm reading a proof for the identity $\det(A) = \det(A^T)$ and I'm trying to udnerstand why the following rows are equivalent: $$\eqalign{ & \det ({A^T}) = \sum\limits_{\pi \in {S_n}} ...
0
votes
0answers
17 views

Fixed points and permutations.

Let $\psi ,\varphi \in {S_n}$ two permutations. Let $M$ a matrix such that $a_{i,j}=1$ iff $i=\sigma(j)$ where $\sigma \in S_n$ ($0$, otherwise) I already showed that $tr(M) = \left| {\left\{ {k \in ...
-1
votes
0answers
31 views

Finding out the triangle numbers [on hold]

How will I find the number of errors without counting the triangle??? DO i have to find out the points and then permutations?
3
votes
0answers
18 views

(Counting problem) more challenging Modular N algebraic eqs - for combinatorics-permutation experts

Experts in algebra please help - Part II after Part I: we would like to know the number of solutions for this set of six of modular N algebraic equations: $$ x_1 y_2 = x_2 y_1 \pmod N \qquad (1) \\ ...
-8
votes
0answers
27 views

No. of 4 digit nos. which can be formed containing at most 2 digits? [on hold]

No. of 4 digit nos. which can be formed containing at most 2 digits? I'm getting $585$ as the answer. Please tell me where I'm wrong: (1.) 9 different digits - 9 nos. (2.) 2 different digits ...
0
votes
2answers
28 views

Number of ways to sit 6 girls and 6 boys together with no two girls together.

As the title of the question explains: What I thought on the very first instant was that we will make them sit alternate hence the answer will be 2 * 6! * 6! But ...
0
votes
1answer
19 views

four digit numbers that have at least one of their digits repeated

The number of four digit telephone numbers that have at least one of their digits repeated is A. 9000 B. 4464 C. 4000 D. 3986
1
vote
1answer
27 views

How many distinct elements does a group of permutation on 3 letters have?

I am having some problems solving a problem similar to this. So i tried making it a more simpler problem. I really don't know how to approach this kind of problem. A hint would be very much ...
1
vote
1answer
26 views

Finding the maximum possible order for an element in $S_5$

I understand that you have to write out all the disjoint cycles and then take the least common multiple which yields the highest order. But my question is, do I have to write all elements of $S_5$, ...
0
votes
3answers
40 views

Forming 4-digit odd numbers under certain rules [closed]

How many four-digit odd numbers can be formed such that every $"3"$ in the number is followed by a $"6"$? A) 108 B) 2592 C) 2696 D) 2700
0
votes
2answers
37 views

finding the password [on hold]

Charlie has forgotten his six-digit ID number. he remembers the following: the first two digits are either 1,5 or 2,6, the number is even and 6 appears twice. if raju uses a trial and error process to ...
0
votes
0answers
29 views

why are these cosets equal?

Please disregard this question until I have uploaded a screenshot K is the subgroup of S_3 defined by the permutations {(1), (123), (132)} They have (1)K = (12)K = {(1), (12)} What they did was ...
0
votes
2answers
33 views

Coloring vertices of a square

Using four colors, red, white, blue and green, in how many ways can the vertices of a square be colored? Assume that reflections and rotations are allowed, meaning that if you examine a square from ...
0
votes
1answer
52 views

Number of seating arrangements in 5 cars

An exercise from Introductory Combinatorics by Richard A.Brualdi: A roller coaster has five cars, each containing four seats, two in front and two in back. There are 20 people ready for a ride. ...
0
votes
1answer
14 views

number of elements in unsortet case

I have a group M with Mn different elements. How many unique combinations can I make out of this in an n digit system when order is no importance. For example if M = {1 2} & n = 3 ...
1
vote
1answer
19 views

How many ways are there to place these books on the shelves?

You are given 5 books and 7 bookshelves. How many ways are there to place these books on the shelves? (The order on the shelves matters.) I want to say $7^5$ since there are 7 possible shelves and ...
1
vote
1answer
25 views

triangles and lines

There are 12 points in a plane. If 4 of them are on a straight line and no other 3 points are on a straight line, then find the difference between the number of triangles and the number of straight ...
0
votes
0answers
13 views

Permutation help arranging letters

How many ways are there to arrange the letters A, B, C, D and E such that A never comes imme- diately after E or D and C always comes immediately before D? Help
0
votes
1answer
15 views

arrangement of balls in bowls

There are five bowls numbered $1$ to $5$. There are $5$ green balls and $6$ black balls. Each bowl is to be filled by either a green or black ball and no two adjacent bowls can be filled by green ...
1
vote
3answers
39 views

Writing a permutation group in 2 row notation

I have a permutation group in $S_7$, namely: $$(12345)(137)(56)$$ How do I write this in two row notation? I am to write it as disjoint cycles and then as transpositions but I feel better working in ...
2
votes
2answers
244 views

How many 90 ball bingo cards are there?

In the UK there are 90 bingo balls. A bingo card consists of 9 columns and 3 rows. A row contains exactly five numbers and four blanks. A column consists of one, two or three numbers and never three ...
0
votes
0answers
27 views

What is this probability that this event could occur?

Records show that 30% of the people, listed as passing the Firefighter's exam in Denver, are republican; the remainder as democrats. Last year, 30 people were hired as firefighters for the city. (25 ...
0
votes
3answers
907 views

No husband can sit next to his wife in this probability question

I have a probability question that reads: Question: If 4 married couples are arranged in a row, find the probability that no husband sits next to his wife. My attempt: ...
2
votes
2answers
71 views

Powers of permutation matrices.

Let $P$ be a permutation matrix obtained by the identity matrix by switching 2 rows $n$ times, (with no two rows switched more than one time). How to show that $$P^{\ n+1} = I$$? Is it true that, ...
0
votes
0answers
18 views

What is total number of inversions in a permutation that is sorted except at indices that are a multiple of a certain number.

So say we have a permutation of integers that is indexed from 0 to n-1, and it is sorted in ascending order except for indices that are a multiple of a number call it x where x is smaller than all ...
0
votes
1answer
27 views

how can you count number of digits used in numbers from -2^127 to (2^(127) - 1)

There are numbers from -2^127 to (2^127)-1. I want to count the number of digits used in all the numbers. For example If I have numbers from -100 to 100 then number of digits used is $2*(1*9 + ...
2
votes
2answers
35 views

Kernel of $\phi:G \rightarrow \operatorname{Sym}(S)$ Group actions

$\operatorname{Sym}(S) == \text{All permutations of the set }S$. Prove $\ker(\phi)=\bigcap_{x\in S}G_x$ where $G_x$ is the stabilizer of $x$. Let $$\phi(a) =\lambda_a(x)=ax \text{ where } x\in S $$ ...
1
vote
1answer
114 views

How many possible combinations in 8 character password?

I need to calculate the possible combinations for 8 characters password. The password must contain at least one of the following: (lower case letters, upper case letters, digits, punctuations, special ...
0
votes
2answers
116 views

Find number of solutions of the equation x1+x2+x3 = 41, where x1, x2 and x3 are odd and non negative integers

There are two constraints to this problem: 1) x1, x2 and x3 are non negative integers 2) x1, x2 and x3 are odd If there had been just the first constraint (non negative integer), i would have ...
11
votes
0answers
111 views

Involutions, RSK and Young Tableaux

Let $S_n$ be the symmetric group on $n$ elements. The Robinson-Schensted-Knuth (RSK) correspondence sends a permutation $\pi\in S_n$ to a pair of Standard Young Tableaux $(P,Q)$ with equal shapes ...
2
votes
0answers
20 views

How many commutative block ciphers are there?

Let $K$ and $M$ and be two finite sets. Let $(G,\circ)$ be the group of permutations over $M$ under composition. Let a (implicitly: block) cipher with key in $K$ and message in $M$ be any application ...
1
vote
1answer
37 views

Number of permutations of AABBBCC, taking 7 letters at a time, when repititions are allowed

What is the number of permutations of the word AABBBCC, taking 7 letters at a time, repetitions being allowed? I think it should be $3^7$, but I can't see why. Also what would be the number of ...
0
votes
2answers
33 views

Difference between permutations

Given the following: 1) Is it wrong to say (1 2 4) (5 3) = (1 2 4) (5 3) or = (3 5) (1 2 3) ? 2) What is meant by ( 1 2 3 4 5 ) and 1 2 3 4 5 ? And why are they not equal? Thanks!
0
votes
1answer
20 views

Permutation Multiplication (easy)

Given α◦β=(1532)(14)(35) How do we get from the given to = ( 1 4 5 2 ) ( 3 ) = ( 1 4 5 2 ) = (4 1 3 5 2) ? Thanks
0
votes
1answer
62 views

List all the permutations of {1,2,3,4}. Which are even, and which are odd?

The answer is: There are 24 permutations. The 12 even permutations are: id , (1 2 3 4) , (1 3 2 4) , (1 4 2 3) , (1 2 3) , (1 2 4) , (1 3 2) , (1 3 4) , (1 4 2) , (1 4 3) , (2 3 4) , (2 4 3). The ...
1
vote
1answer
33 views

number of ways of constructing $n\times2$ rectangle from a $1\times2$ rectangle

You are given $1\times2$ rectangles and you have to construct an $n\times2$ rectangle from it. Tell the number of ways of constructing $n\times2$ rectangle from a $1\times2$ rectangle
2
votes
2answers
42 views

A man, woman, boy, girl, cat, and dog are walking down a path..

I'm hoping someone can explain how this works. The problem: A man, woman, boy, girl, cat, and dog are walking down a path in single file. How many ways can this happen if the dog is between the man ...
1
vote
0answers
15 views

Composing permutations in factorial notation

Given two permutations $p_1$ and $p_2$ in factorial notation, is there a direct algorithm which computes their composition directly, i.e. without translating to a different notation or via computing ...
0
votes
0answers
23 views

Number of permutations with double restriction

Task is as follows: Let's have 6 element set, there are obviously $6!$ permutations of this set, but there are two restrictions: element 1 and 2 have to be in one cycle and element 3 can't be with 1 ...
0
votes
2answers
26 views

How many good words are there?

A “good” word is any seven letter word consisting of letters from $\{A,B,C\}$ (some letters may be absent and some letter can be present more than once), with the restriction that $A$ cannot be ...
1
vote
1answer
34 views

Why is this the method to getting transpositions from disjoint cycles?

I have the disjoint cycle: $$(156)(2437).$$ Apparently the "method" would get us: $$(1,6)(1,5)(2,7)(2,3)(2,4).$$ Basically you take the first number, and put it as a transposition of the last number ...
0
votes
0answers
21 views

A coin is tossed m+n times.(m>n) How many outcomes have at least m consecutive heads?

The problem I face is(obviously for which the question was intended) that, suppose $m=3$,$n=2$, then ${HHH,H,T}$ and ${H,HHH,T}$ are same while ${HHH,T,H}$ and ${H,T,HHH}$ are different. Hence, I ...
0
votes
3answers
240 views

In how many ways can an animal trainer arrange 5 lions and 4 tigers in a row so that no two lions are together?

Problem : In how many ways can an animal trainer arrange 5 lions and 4 tigers in a row so that no two lions are together? 1st Approach : L T L T L T L T L The 5 lions should be arranged in the ...
2
votes
1answer
36 views

How many ways can six of the letters of the word ALGORITHM be selected and written in a row if the first letter must be A?

As the title states, the question is: "How many ways can six of the letters of the word ALGORITHM be selected and written in a row if the first letter must be A?" I don't really get what the problem ...