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

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1answer
15 views

Why $c(a_1 a_2 … a_k)c^{-1}$ is the k-cycle $(c(a_1) c(a_2)… c(a_3))$?

If $a,b,c \in S_n$, why $c(a_1 a_2 ... a_k)c^{-1}$ is the k-cycle $(c(a_1) c(a_2)... c(a_3))$? (I need this to prove that two permutations are conjugate iff they have the same cyclic structure.)
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2answers
17 views

probability of picking up two m&ms of same color randomly

There are 3 red m&ms, 5 green m&ms, and 8 blue m&ms. If I pick two m&ms out randomly, what is the probability of me picking two m&ms of the same color? I'm not sure if this is ...
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0answers
28 views

Baseball Permutations Problem [duplicate]

Asked question before and got advice wondering if I am in the right direction. Two part question (My work below). For both questions will use the orioles current roster: -Current orioles roster: 12 ...
0
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1answer
20 views

Pet Store Problem?

Hi I answered the problems just wanted to verify if my approach was correct. Any suggestions appreciated. Question: A pet store has 6 puppies, 9 kittens, 4 lizards, and 5 snakes. a. If you select a ...
0
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1answer
38 views

Baseball Combinations Problem

Two part question (My work below). For both questions will use the orioles current roster: -Current orioles roster: 12 pitchers, 2 catchers, 5 in-fielders, and 6 out-fielders: Similar to the list ...
1
vote
0answers
26 views

A Baseball Combinations Problem [duplicate]

My answer I got: 11,750,400 (Work below) Question: Given the current orioles roster: 12 pitches, 2 catchers, 5 in-fielders, and 6 out-fielders Buck Showalter (the Orioles manager) needs to select 10 ...
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2answers
31 views

Combinations and Probability Problem

So far I got up to part C and I think I have to maybe divide my answer from part B by some number but am totally confused on how to approach this question. There are 15 dogs in an obedience class. ...
3
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1answer
15 views

No normal subgroup of a subgroup of $S_n$ imply the subgroup is the one of even permutations or consists of two elements

The following is an old exam question from a n introduction to group theory course: Let $G$ be a proper subgroup of $S_{n}$, $n\geq3$. Prove that if $G$ does not have any non-trivial normal ...
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0answers
23 views

Catch the fraud! [migrated]

Ok now this is one tough math question but fun to try. If this site does not tolerate such matter please let me know and I'll remove this. There are 10 gold smiths in the town and a rich businessman ...
0
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1answer
16 views

Prove that $L_7$ is a subgroup of $S_7$

Let $\sigma(v)$ denote the signature of the permutation $v$. Is the subset $L_7 = \{v\in S_7 : \sigma(v)=-1\}$ a subgroup of $S_7$? I am not sure I am proving it the right way. To prove that ...
0
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1answer
24 views

Nonnegative integer solutions

How many non negative integer solutions are there to the equation: $(2*X_1) + (2*X_2) + X_3 + X_4 = 12$?
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1answer
24 views

more how many different possibilities stuff in a row

There's 4 green m&m, 5 red m&m, 8 blue m&m, 10 yellow m&m. In how many ways can you line them all up in a row. I believe the answer is 25840847132100 from an online total combinations ...
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3answers
27 views

permutation question about stuff in a row [on hold]

You have 10 dogs in total, 4 of which are samoyeds, which you can't distinguish between. The other 6 are all distinct breeds. Given that, how many different possibilities can all 10 dogs be lined up ...
0
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1answer
20 views

Show that a cycle of length $p$ and a cycle of length $q$ in $S_n$ are conjugate if and only if $p = q$.

Show that a cycle of length $p$ and a cycle of length $q$ in $S_n$ are conjugate if and only if $p=q$. First of all, I'm a bit confused about the meaning of '... are conjugate'. Does this mean that ...
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2answers
29 views

Shortest possible way to go from one corner of the city to opposite corner if a city has $n,m$ parallel roads from east - west & north -south?

Let us suppose there is one city which has $n$ parallel roads running East - West and $m$ parallel roads running North - South. Now let us take that the distance between every consecutive pair of ...
2
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0answers
51 views

Permutation problem with ordering persons in a line

We have the following problem: There are $p$ persons from each city. Consider $p \cdot n$ persons from $n$ different cities. The $p \cdot n$ persons stand in a line such that every person stands next ...
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2answers
15 views

How many parallelograms can be formed when a parallelogram is cut by $2$ sets of $n$ parallel lines?

A parallelogram is cut by two sets of n parallel lines parallel to the sides of the parallelogram. The number of parallelogram thus formed is..?? I think we can do it by combinatorics.. But I'm not ...
3
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2answers
34 views

14 pencils handed out to 6 people. Each person has at least 1 pencil. Person 6 no more than 3 pencils.

We have 14 indistinguishable pencils and we want to hand out all of the pencils to 6 people and we want everyone to get at least one pencil. However, we do not want person 6 to get more than 3 ...
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2answers
38 views

How many different ways can 14 pencils be passed out to 6 different people? Some people are allowed no pencils.

There are 2 questions that are very similar and I have the same answer to both but I don't think that's correct. Can you help me see the difference between the 2 questions. We have 14 ...
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5answers
420 views

What's wrong with my permutation logic?

The given question: In how many ways the letters of the word RAINBOW be arranged, such that A is always before I and I is always before O. I gave it a try and thought below: Letters A, I and ...
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0answers
54 views

Sign Of Permutation [on hold]

Why can $\operatorname{Sgn}(\sigma\circ\tau)$ be written as: $$\prod\limits_{i<j} \frac{\sigma\circ\tau(j)-\sigma\circ\tau(i)}{j-i}$$ It has something to do with the fact that permutation is a ...
0
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1answer
21 views

Find the population size that maximizes the probability that two random samples of size $20$ will have exactly $2$ members in common

Ten fish are caught in a lake, marked, and then returned to the lake. Two days later 20 fish are again caught, 2 of which have been marked. (a) Find the probability of 2 of the 20 fish being marked ...
2
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2answers
40 views

What is the permutation representation of $SL_2(\mathbb{F}_p)$, $PSL_2(\mathbb{F}_p)$ and $GL_2(\mathbb{F}_p)$?

It seems that there is a action by which $SL_2(\mathbb{F}_p)$ and $GL_2(\mathbb{F}_p)$ permute the $p^2$ ordered tuples in $\mathbb{F}_p^2$. What is the map from the $2 \times 2$ matrices over ...
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0answers
28 views

Permutation as a product of generators of the permutation group

Let $G$ be a permutation group, generated by $g_1,\ldots,g_n$. And let $h$ be in $G$. Example: $G=\langle (12)(34),(123)\rangle$ and $h=(12)(34)(123)=(243)$ (reading the cycles from right to left, ...
0
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0answers
15 views

Conjugation in Symmetric Group [on hold]

For $\alpha = (1 3 4 6)(5 8 9)$ and $\beta = (2 3 7)(9 1 8 5)$, compute $\alpha\beta\alpha^{-1}$ ? I read a couple of solutions, but I don't really understand how to solve it. Thank you
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2answers
26 views

A permutation and combination question (plus summation of a series)

A student is browsing in a second-hand bookshop and finds $n$ books of interest. The shop has $m$ copies of each of these $n$ books. Assuming he never wants duplicate copies of any book, and that he ...
0
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1answer
28 views

how to find the number of different arrangements when a coin is thrown 12 times and gets 5 heads

Suppose a fair coin which has 2 faces-Head(H) and Tail(T) is thrown 12 times and we get exactly 5 heads: $$H,H,H,H,H,T,T,T,T,T,T,T$$ How can I find the number of different arrangements it can have? ...
1
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1answer
48 views

Find the conjugacy classes of $A_5$

I was trying to find the conjugacy classes of $A_5$. So I started by writing out all the conjugacy classes of $S_5$ in the hope that I could just restrict the set of them. The conjugacy class ...
1
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1answer
32 views

Permutation of pencils in box

You have 3 red, 4 blue and 5 green pencils. How many ways are there, to arrange all these pencils in box, with condition, that none of blue pencils are adjacent to each other? Okay: Let's arrange ...
2
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1answer
33 views

Burnside's Lemma implementation

Can someone please explain to me what Burnside's Lemma theory is about, how to understand if a situation or problem calls for the use this theory? I went through the wiki page but could not grasp the ...
1
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2answers
78 views

How many zeroes are there at the end of $36!^{36!}$?

Could you please tell me how many zeroes are there at the end of $36!$ to the power $36!$, i.e., $36!^{36!}$? I have been trying to find out. Read some reviews and answers related this but didn't ...
0
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0answers
75 views

Number of m letter pairs with a vowel in the alphabet

The number of ways to choose m unique pairs of letters from the alphabet is: $$ \frac{26!}{(26-2m)! m! 2^m} $$ Which gives 325 single pairs, 44850 double pairs, 3453450 triple pairs... If I want to ...
0
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1answer
27 views

How many ways to order 26 letters so that the strings lift and graph are not included?

I just need to subtract the letters used by the strings? or is just removing the ordering of the words?
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2answers
46 views

Number of possible 4 digits number

I was solving a question paper and i stuck due to some missing concepts. please help me out.I want the shortcut to solve this type of question too. Question:Find the number of all four digit numbers ...
2
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1answer
23 views

Summation to count number of strings over N characters?

How many different strings of five characters are there if only lower-case letters or numbers can be used in creating these strings? Here is my solution: There are 26 letters in the alphabet ...
3
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1answer
78 views
+50

Permutations containing a given subsequence

Let $f(n)$ denote the number of $4n$-long strings formed from $2n$ a's and $2n$ b's, such that the string contains, as a (possibly non-consecutive) subsequence, a pattern containing $n$ a's and $n$ ...
0
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1answer
24 views

How many permutations of $x^5 + y^5 + z^5$ are possible given x, y, z are integers such that $1 \le x \le y \le z \le 180$?

I initially thought it would be $180^3$ possible permutations, but then quickly realized that something like $x=3, y=2, z=1$ would not be valid due to the constraints. How can I go about trying to ...
1
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1answer
24 views

How to solve this equation containing $P(n,r$)?

$P(n,r) := \frac{n!}{ (n-r)!}$ The equation is: $P(n,r) = 42 P(n,3)$ I need to clear the variable $n$. It doesn't matter that it has to be expressed as a function of $r$. I cannot pass the step: ...
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1answer
23 views

Arrangement of the word MATHEMATICS if last spot must have the letter 'T'

How many ways can the word MATHEMATICS be arranged if the last letter must be a T? My solution: There are $2$ possible choices for the last letter (There are $2$ different T's), which leaves $10$ ...
0
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1answer
26 views

Partially ordered permutations

If I have a set $X$ of length five such that $X=\{1,2,3,4,5\}.$ I want to find the number of permutations where the relative order of the $2$ sets $\{2,4\}$ and $\{2,5\}$ is maintained. In other ...
0
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1answer
17 views

Is this relation P an equivalence relation or a partial order relation?

I am having trouble with partial order and equivalence relations. I was wondering if someone can guide me through this problem. Let $Σ$ be the set of letters {$a, b, . . . z$}. Let $Σ^∗$ be the set ...
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0answers
22 views

Quotient Groups with symmetric $S_4$ group [duplicate]

I'm working on this problem and I am having trouble figuring it out. The problem is: Find the quotient group $G/H$. Write out the distinct elements of $G/H$ and construct a multiplication table of ...
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0answers
12 views

Help needed for statistical analysis of pitch class sets

Within Music Analysis, there is a quite mathematical type of analysis which looks at pitch class sets ($pcs$), not surprisingly known as pitch class set analysis. See ...
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1answer
26 views

Permutations and Combinations 2

The word ARGENTINA include the four consonants R,G,N,T and the vowels A,E,I How many of the arrangements have a consonant at the beginning,then a vowel,then another consonant at the beginning,then a ...
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2answers
13 views

Permuations and Combinations problem

A football team consists of 3 players who play in a defence position, 3 players who play in a midfield position and 5 players who play in a forward position.Three players are chosen to collect a gold ...
1
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1answer
25 views

indecomposable permutation

we say the permutation $\sigma = a_1 \dots a_n \in S_n$ is indecomposable if ${a_1 , \dots a_j} \neq [j] ,\forall j<n$. let f(n) be the count of the indecomposable permutations in $S_n$. show: ...
3
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1answer
20 views

Selecting “either representative” Permutation

A Chess club consisting of $14$ Math majors, $11$ EE majors and $11$ CS majors. In how many ways can the club select a president and vice president if either the president or the vice president must ...
4
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1answer
49 views

Permutations and Combinations exam question

Before I proceed with my queries I think it's best to present the question at hand. A class consisting of 4 males and 12 females in randomly divided into 4 groups of 4. What is the probability ...
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3answers
29 views

Proving $AD_1A^{-1}=D_2$

I want to prove that if $A$ is a permutation matrix, and $D_1$ is diagonal, than $AD_1A^{-1}=D_2$ where $D_2$ is also a diagonal matrix. I have worked out that $A^{-1}=A^T$ and I can see that the ...
2
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0answers
11 views

Nice embedding of the permutohedron of order $n$ in ${\mathbb R}^{n-1}$

The permutohedron $P_n$ of order $n$ ($n\geqslant 2$) is the convex hull of the points $P_\pi=(\pi(1),\dots,\pi(n))$ where $\pi$ ranges over all permutations of $\{1,2,\dots,n\}$. Obviously, since ...