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

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1answer
13 views

How many 2m-permutations, consisting only of cycles of even length?

How many 2m-permutations, consisting only of cycles of even length? I have found this formula: $$Q_2(n) =((2n − 1)!!)^2$$ but how it can be proven?
0
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1answer
19 views

fixed length of permutaions cycles

How much permutations has only 10 cycles, but three of them has length 3 and seven of them has length 7?
0
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1answer
8 views

Permutation test and p-value

I construct a permutation test in order to see If two samples come from the same distribution or not. I have two vectors $x, y$ that hold values of sampled values from two populations and the test ...
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0answers
13 views

Types of ordering

Can somebody please help me understand how ordering of numbers work? There are 3 types of ordering I want to understand. Lexicographic, reverse lexicographic and Fike's ordering. How would the ...
0
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1answer
33 views

Problem Solving Involving Permutation

Find the number of 6-digits number with no 3 consecutive number with same digits. Note that 0 might be the first number. I have tried to find the number with no pairs, 1 pairs, 2 pairs and 3 pairs. ...
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1answer
32 views

example for permutizer group

permutizer of a subgroup H of G is defined to be the subgroup generated by all cyclic subgroups of G that permute with H. You can help us give an example?
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0answers
29 views

Multi-ruled combinatorics problem (need this for my lab)

I need to know this for practical purposes and not homework, learning etc.. Say I have 3 electrodes A,B and C. Say I also have 3 electrolytes A,B and C. If electrode A has to be in electrolyte A, ...
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2answers
57 views

Combinatorics homework problem [on hold]

In how many ways can $23$ different books be given to $5$ students so that $2$ of the students will have $4$ books each and the other $3$ will have $5$ books each?
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2answers
37 views

let $D_n$ be the number of permutations of $\{1,2,3,…n\}$ which leave no element fixed.

Let $n\geq2$ and let $D_n$ be the number of permutations of $\{1,2,3,\dots,n\}$ which leave no element fixed. How to write an expression for $D_n$ in terms of $D_k$? I don't know how to start. Please ...
1
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1answer
48 views

Unique permutations from set with repetitions

I am new to combinatorics and might ask a trivial question: There are $69$ different items, each present $4$ times. From this total of $276$ items, $20$ should be picked at random. I need the formula ...
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2answers
29 views

Possible 4 character passwords involving a letter and a digit.

A password consists of 4 characters, each of which is either a digit or a letter of the alphabet. Each password must contain at least ONE digit and AT LEAST ONE letter. How many different such ...
2
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0answers
39 views
+200

How many permutations do we need before we're in $SU\left( n\right)$?

Let $\mathcal{L}\subseteq \mathfrak{su}\left( n\right)$ be a Lie algebra for $n \geq 2$ with Lie group $G = e^{\mathcal L}$, and let $X \in G$ be represented by an $n\times n$ matrix (I prefer fixing ...
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1answer
26 views

How many different teams can be created between two groups?

If a company has 8 painters and 12 electricians. How many different teams can be created with 1 painter and 1 electrician? I know that the number of ways a team can be made is: $ {8 \choose 1} * ...
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1answer
18 views

number of possible outcomes in a license plate with conditions [on hold]

howmany license plates can me made when a) first two letters are different and the rest different digits e.g. DA3457 b) two letters in alphabetical order and the digits increasing e.g. CD1234
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2answers
10 views

compute the number of permutations

Compute the number of permutations of $\{1,2,3,4,5,6,7,8,9\}$ in which either $2,3,4$ are consecutive or $4,5$ are consecutive or $8,9,2$ are consecutive. I know we will use some exclusion-inclusion ...
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0answers
17 views

Question about permutation.

Suppose a and b are permutations of the same cycle type. Why aligning them on top of one another and interpret it as a two line representation of permutation gives me a permutation that will conjugate ...
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0answers
41 views

In how many ways 3 persons can solve N problems.

There are $3$ friends $(A,B,C)$ preparing for math exam. There are $N$ problems to solve in $N$ minutes. It is given that: Each problem will take $1$ minute to solve. So all $N$ problems will be ...
1
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1answer
30 views

What is the probability of not rolling any given number on 10 rolls of a die?

In other words, ALL combinations which don't contain at least one of the number from 1-6 would count. So for example... 5, 2, 3, 3, 4, 1, 5, 5, 3, 1 would be counted because there is no 6 Also 5, ...
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1answer
64 views

Better Explanation for an already posted question [duplicate]

Can anyone explain why in this question the answer is 5! * 2! * 10P3? I understand the 5! and 2! but for 10P3 the first thing I thought of was 3! Thanks.
2
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0answers
42 views

permutation of the word INTERMEDIATE [on hold]

IF the letter of the word INTERMEDIATE are permuted then in how many ways 1) N comes before M and M comes before D 2) Exactly four letters come in between M and N
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2answers
17 views

Permutation Question Help

Hexadecimal numbers are made using the sixteen digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F. They are denoted by the subscript 16. For example, 9A2D$_{16}$ and BC54$_{16}$ are ...
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1answer
20 views

The order of a cyclic subgroup, generated by a permutation

I was wondering, how can I prove that all cyclic subgroups generated by a permutation, has the same order as the permutation? For example, cyclic subgroup $\langle(---)\rangle$ will have order 3. So ...
2
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2answers
46 views

Number of 8 character passwords including numbers and letters without repetition

A password must be created with 8 characters. It can use number or letters, but they cannot be repeated (and letters are not case sensitive so we have only 36 characters). How many passwords are ...
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3answers
30 views

Calculating the probability of receiving all possible rewards after 15 events

I encountered this question in my Data Management and Statistics textbook. I tried to calculate the probability using binomial theorem and combinations/permutations, but I could only get close to the ...
0
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1answer
23 views

what is the probability that the real estate agent can get into specific home ???

A real estate agent has 8 master keys to open several new home. Only 1 master key will open any given house. If 40% of the homes are usually left unlocked what is the probability that the real estate ...
0
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1answer
26 views

How many different ways can a student check off one answer to each question?

If a multiple-choice test consists of 6 questions each with 4 possible answers of which only 1 is correct, In how many different ways can a student check off one answer to each question ?
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2answers
17 views

Counting number of ways in poker game

What is the total number of ways in which the poker hand is full of house that is you have to pick 5 cards out of 52 cards such that it contains exactly 3 cards with the same value. Example a card ...
3
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2answers
27 views

Cycle structure in a symmetric group

I have a bit of a problem. I'm currently reading about permutations, and I have a little exercise that asked me to find all cycle structures in $S_6$. I came up with the following $ ( -)\\ (- -)\\ (- ...
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2answers
32 views
-4
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0answers
28 views

If 1<=r<=n, then prove that C(n+1,r-1) = (n-r-1) C(n,r-1) [closed]

The question is related to permutations and combination, If 1<=r<=n Prove the following theorem $\dbinom{n+1}{r-1} = (n-r-1) \dbinom{n}{r-1}$.
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1answer
33 views

Permutation of Groups - looking for the right term

I'm looking for more detailed information about the following problem, but i'm missing a right keyword, or term for this: Let's assume i have 10 people and they are assigned to groups: ...
0
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1answer
33 views

Represent a bijection using a permutation

Let $X = \{1, 2, 3, 4, 5, 6, 7\}.$ For every $n \in X$, write $n^2 - 3n^5 = 7q_n + r_n, 1 \leq r_n \leq 7.$ Define a function $f: X \to X$ by $f(n) = r_n.$ (a) Find an element $\alpha \in S_7$ that ...
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2answers
119 views

Arranging books on the shelf.

There are five distinct computer science books, three distinct mathematics books, and two distinct art books. In how many ways can these books be arranged on a shelf if no two of the three mathematics ...
0
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1answer
22 views

Select K numbers from N numbers fairly

I want to fairly select K numbers out of an array of N number. I know that this problem can be solved using Reservoir Sampling but I want to know if this approach is correct too? ...
0
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1answer
36 views

Permutation (inclusion-exclusion)

2 corrected exams are being returned to each of n students. How many ways can the teacher give those 2 exams back to each student such that everyone receives at least 1 exam that is not his. I know ...
0
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1answer
12 views

How many sequences of length N squared can be formed with N different values where each value is used exactly N times?

For instance, for N=2, the answer is 6 (e.g. aabb, abab abba baab baba bbaa). For N=3, the answer is 1680. I'm looking for the proper formula. Thanks
2
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0answers
14 views

Is there an effective way to convert a product of 2-cycles into a product of n cycles?

I came across this problem that asks me to convert (12)(34) into a product of 5 cycles. After testing for many different combinations i get (12345)(14352)(12345). The way I do it is this: ...
0
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0answers
16 views

What's the rank of a matrix that has constant number ones in each col/row over $F_2$

Let $A$ denote a $n\times n$ matrix over $F_2$, which means $A \in \{0,1\}^{n\times n}$. Also assume that each row and each column only has exactly 3 ones. 1) What is the upper bound and lower bound ...
1
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1answer
38 views

Strategy for number of non-negative integers solutions such that $x_1+x_2+\frac{\enspace\enspace\enspace}{}+x_5 = 50$

I'm trying to figure out the number of solutions to the following problems, although I'm not entirely sure what strategy I should use to solve these. Combinations of non-negative integers ...
2
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2answers
23 views

Permutations and school timetable

If there are 6 periods in each working day of a school. In how many different ways can one arrange 5 subjects such that each subject is allowed at least one period? I tried this way- One of the six ...
0
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3answers
40 views

Permutations in products of disjointed cycles

How do I calculate the following permutation in the symmetric group $S_6$ giving the answers as products of disjoint cycles: $$(2,3,5,6)(1,6,2,4)$$ I have tried following this question but I don't ...
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2answers
21 views

Permutations and combinations - how many ways to select? [closed]

From eight persons A, B, C, D, E, F, G, H, four has to be selected such that if A is selected, B also has to be selected. How many this can be done?
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0answers
12 views

No of different permutations .. a recurrence relation needed

Given N similar red balls and M similar white balls. In how many different ways they can be arranged so that ...
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2answers
23 views

Strategies for solving permutations of a word

So I'm trying to prepare for exams, and am having some trouble with permutations, and was wondering what's a good strategy to solve this task is: Given the set of letters $\text{AAABBBBCCDEEFG}$ ...
0
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2answers
27 views

Number of different possible permutations of a telephone number

A telephone number consists of $10$ digits, all from $0$ to $9$. The first digit is $0$. The remaining digits can be any number ranging from $0$ to $9$. How many possible telephone numbers are there? ...
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2answers
105 views

Permutations / Combinations - suppose a word is a string of 8 letters of the alphabet with repeated letters allowed

1.) How many words are there? Not sure how to solve this since repeated letters are allowed. $n^r$ is the formula we are told to use for permutations with repeated objects, but $26^8$ seems like too ...
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1answer
22 views

Combinatorics problem

I am trying to solve this question, my solution involves solving a combinatorial problem as follows : Number of arrangements of exactly k distinct elements in n slots such that each one of the ...
2
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0answers
33 views

Concerning cycles and group actions.

Here is the problem that I have. Let $C=\{a=(ijkl)\}$ be the set of all cycles of length 4 in the symmetric group $S_4$. $S_4$ acts on the set $C$ by conjugation. For every cycle $a\in C$ determine ...
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3answers
212 views

Combinations of pizza toppings with at least one vegetable and at least one meat.

Here is a question from my quiz: Superior Pizza has seven vegetable ingredients and nine meat ingredients. The number of ways to select five ingredients (no doubling on ingredients) with at ...
0
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2answers
36 views

Combinations - 17 women and 21 men to form a committee of size 7

How many committees are possible if a committee must have $3$ women and $4$ men? $_{38}C_3+_{38}C_4$ or $\frac{38!}{3!35!}+\frac{38!}{4!34!} = 8,435+73,815 = 82,251$ How many committees are possible ...