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

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Finding expectation and variance of a selection of three balls out of six?

I just asked this question, but worded it wrong so while the given answers are useful, they still leave me confused for where I am in the progression through my stats book. My problem is I've got 3 ...
0
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1answer
8 views

permutations with specified repetition counts [duplicate]

Problem: Determine the number of permutations of the characters for: AABBBC How can I calculate a problem like this generally, given a set of characters and a number of times each has to appear?
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1answer
19 views

Repeated Permutations

In school we have been studying combinations and permutations, and in a programming assignment I was testing points on a coordinate plane. Testing all integer points surrounding the point (0,0) you ...
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2answers
20 views

Permutation Problem need help [on hold]

So there is 7 people seated at a circular table. Person A cant move. How many ways can they be seated If person A stays in their seat?
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0answers
58 views

Is this an action of $S_{n}$ on $\mathbb{R}_{n}$?

I am trying to prove that $S_{n}$ acts on $\mathbb{R}_{n}$ with the map $$* : S_{n} \rightarrow \mathbb{R}_{n}, \quad * \left( \sigma, \left( r_{1}, r_{2}, \dots, r_{n} \right) \right) = \left( ...
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1answer
33 views

How many ways can $6$ pencils be distributed between $2$ boys if each boy gets at least one pencil? [on hold]

The number of ways in which 6 pencils can be distributed between 2 boys such that each boy gets at least one pencil is?
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1answer
18 views

Finding The Number Of Inversions In A Permutation

Let the be the following permutation: $(1 5 4)(3 6)\in S_6$ How do I count the number of inversions to calculate the sign of the permutation? $(1 5 4)(3 6)=(1 5)(1 4),(3 6)=3$ so it has an ...
2
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2answers
45 views

Number of strings [on hold]

There are $2^{10} =1024$ possible $10$ -letters strings in which each letter is either an $A$ or a $B$. Find the number of such strings that do not have more than $3$ adjacent letters that are ...
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2answers
42 views

Number of ways in which a batsman can score 14 runs in 6 balls not scoring more than 4 runs in any ball.

Hello everybody my query is regarding the number of positive integral solution. In the sport of cricket, find the number of ways in which a batsman can score $14$ runs in $6$ balls not scoring ...
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0answers
30 views

How to find the no. Of non negative integral solutions of a equation

I want to find the no. Of non negative solutions of $X+2y+3z=n$ I know how to find the non negative integral solutions of the equations of type $X+y+z=n$ using dividers method that is assume that ...
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1answer
52 views

Equivalent permutation representations.

The definition of Equivalent Permutation Representations that is defined in "A course in Theory of Groups" by Derek Robinson Suppose we have group $G$ has permutation representation on set $X$ and ...
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1answer
11 views

Show that each conjugacy class has a particular value for probability after k steps

I have a permutation group $S_n$ and am performing random transpositions on them. Now there will be a bunch of conjugacy classes as a result of that. P_k_s is the probability that after k ...
0
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1answer
14 views

How many different sets of 8 elements can I pick if I am picking from a bag of 1681 elements probability and counting [on hold]

I have 1681 points and trying to see how many different constellation of 8 points I can have to see if it is feasible to try out all possibilities to find the best. It's actually a Communication ...
0
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0answers
13 views

number of permutations that have $i<j$ against the ones with $j>i$

Consider a set $A=[a_1,a_2,\dots,a_n]$ and its all possible permutations $P$. Select one permutation $\sigma=(\sigma(a_1),\sigma(a_2),\dots,\sigma(a_n)\ )\in P$ and consider a set of distinct pairs ...
0
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0answers
8 views

Sign Of Permutation That Is Written As C Different Cycles

prove: if $\sigma\in S_n$ is a factorization of $c$ disjoint cycles so $Sgn(\sigma)=(1)^{n-c}$ We know the one cycle sign is $(-1)^{l-1}$ so $c$ of them is $(-1)^{l-1}\cdot ...
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1answer
22 views

How many $(r+1)$- subsets of $[n+1]$ have $(k+1)$ as their largest element?

Let $[n+1]$ be the set defined by $[n+1]=\{1,2,\ldots,n+1\}$. Call a subset of $[n+1]$ with $r+1$ distinct elements an $(r+1)$-subset. How many $(r+1)$-subsets of $[n+1]$ have $(k+1)$ as their ...
3
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1answer
45 views

A fair die is rolled nine times. What is the probability that 1 appears three times, 2 and 3 each appear twice, 4 and 5 once and 6 not at all?

A fair die is rolled nine times. What is the probability that 1 appears three times, 2 and 3 each appear twice, 4 and 5 once and 6 not at all? My approach is fairly simple. The dice is fair, so we ...
0
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1answer
19 views

For a given set of pairings in the 8-team basketball tournament,in how many ways can the top 3 positions in the final standings be filled?

The top 2 teams must be from different brackets. I couldn't understand the question.In the initial competition,8 teams are separated into 4 groups(with 2 teams each) to compete.And it will give 4 ...
0
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1answer
17 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
27 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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1answer
118 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 ...
2
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1answer
161 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 ...
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2answers
151 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
16 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
18 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 ...
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1answer
33 views

Ho many nonnegative integer solutions does the equation $2x_1 + 2x_2 + x_3 + x_4 = 12$ have? [on hold]

How many nonnegative integer solutions are there to the equation: $2x_1 + 2x_2 + x_3 + x_4 = 12$?
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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 ...
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1answer
23 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
34 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
55 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
20 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 ...
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2answers
42 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
39 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
423 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
60 views

Sign Of Permutation

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
24 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
43 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
31 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, ...
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0answers
15 views

Conjugation in Symmetric Group [closed]

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? ...
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1answer
51 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
35 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 ...
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2answers
81 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
77 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 ...
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1answer
28 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
47 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 ...