0
votes
2answers
34 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 ...
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
28 views

Using permutations to determine whether given arrangements of the “eight puzzle” are possible.

The "eight puzzle" is a reduced 3x3 version of the 4x4 "fifteen puzzle", which is a very simple game which involves sliding 15 numbered tiles around 16 places, with one free space always being ...
0
votes
1answer
32 views

Showing that there is a permutation $\rho$ that fixes a number that $\sigma$ moves when $\rho \sigma \rho^{-1}=\sigma^{-1}$

Doing an assignment, getting a bit frustrated with this exercise, would really appreciate some help. The first exercise explains what $\sigma$ and $\rho$ are: Let $\sigma$ be the $r$-cycle ...
1
vote
1answer
44 views

Using that $G$ is isometric to a subgroup of $S_G$ to prove something about $G$

I am doing the following exercise for an assignment: Assume that $G$ is any finite group with non-trivial elements such that $bab^{-1}=a^{-1}$. Let $k$ be a natural number and use induction to ...
3
votes
3answers
81 views

How many different 4 digit combinations will include at least one 7, assuming numbers cannot repeat

I cannot get the correct answer - $2016$. What I have tried so far is thus: the number $7$ can occur $1, 2, 3,$ or $4$ times. Since it is a combination we do not care if the number starts with zero ...
3
votes
3answers
166 views

What does “order matters” regarding permutations refer to?

I psychoanalyze EVERYTHING and permutations/combinations are frustrating me. Sorry for posting so many questions lately but I really appreciate all of the help! Ok so I know the permutation formula: ...
0
votes
1answer
26 views

Can someone please explain the reasoning for this permutation problem?

I'm studying and reading through my discrete math book.. I seemed to be grasping the idea of permutations, but I don't understand how the solution for this particular problem came to be. Question: ...
2
votes
2answers
59 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 ...
0
votes
1answer
20 views

Permuation & combination on finding number of ways lid can be wrongly placed

There are 5 bottles of sherry and each have their respective caps. If you are asked to put the correct cap to the correct bottle then how many ways are there so that not a single cap is on the ...
0
votes
1answer
39 views

Just double checking if I am doing this correctly.

A professor writes 40 discrete mathematics multiple choice questions each with three possible answers, a), b), or c). If there are absolutely no constraints on how many questions can have answer a) or ...
1
vote
1answer
27 views

How do I find “at most” x bit strings of length 20?

I tried searching online and I found several examples of doing such problems, but I'm still not sure if I'm doing them correctly and would greatly appreciate some help! How many bit strings of length ...
0
votes
2answers
33 views

Permutation Problem with Given Numbers

Given the digits 0,2,5,6,9. A. How many 3-digit numbers can be formed if no two digits are to be the same? B. Of the numbers formed, how many are even? How many are odd? How many are greater than 600? ...
1
vote
3answers
23 views

Different arrangements - Permutation

Into how many different arrangements that look different can three identical trigonometry books, 4 identical calculus books, 5 identical algebra books be placed on a shelf?
0
votes
2answers
27 views

Writing a Permutation as a product of Disjoint Cycles

Write the following as a product of disjoint cycles: $(1 3 2 5 6)(2 3)(4 6 5 1 2)$ I know from my solutions guide that the answer is: $(1 2 4)(3 5)(6)$ but I don't know how to do that. I started ...
0
votes
1answer
22 views

combinatorics :: selecting from variety of groups

in how many ways one or more than one fruit can be selected from 6 varieties of fruits given that there are 5 fruits of each variety? MY TRY : i dont have any clue so i am giving my thoughts MY ...
3
votes
1answer
94 views

Distributing $n$ different things among $r$ persons

How can $10$ different pencils be distributed among $3$ students? MY TRY $1$ total ways $= 3^{10}$ MY TRY $2$ $10 \times 9 \times 8 =720$ Which one is correct? If both are wrong what is correct ...
0
votes
2answers
42 views

Permutation Homework

There are two teams.Two games were played.There are three possible outcomes which are win, lose or draw. how many permutations are there?
1
vote
2answers
29 views

Partioning/Enumeration

How many ways can one distribute A) 15 Balls into 3 bags. Both bag and balls are distinct (labelled) and each bag must contain at least one ball. B) 10 balls into 3 bags. again both bag and balls ...
0
votes
2answers
137 views

Permutation & Combination card sequence . .

I've been trying to do these 2 questions about Permutation & Combination which linked to card play. Q1 says : ...
1
vote
2answers
119 views

combination and permutation !!!!

I have 3 questions that i had a try to do but i didn't understand them could anybody please help me to solve these questions. For Q1 i know how to use the multiplication counting procedures for a) i ...
1
vote
4answers
62 views

Permutation on word if E,F,G have to stay in order

Im stuck on a problem which I have answered and need help to verifiy if I have done/understood it correctly. Problem If we have the following string: ...
1
vote
2answers
97 views

How many $7$ digits number can be made?

How many $7$ digits number can be made with $1,2,3,4,5,6,7$ so that they are divisible by $11$? (Repetition is not allowed.) I know the divisibility rule of $11$, so the main problem is counting.
3
votes
1answer
52 views

How to arrange $n$ pairs of numbers so that this expression is minimized

Consider $n$ pairs of positive integers, $(x_1, y_1), (x_2, y_2), \dots, (x_n, y_n)$. Make a permutation $(a_1, b_1), (a_2, b_2), \dots, (a_n, b_n)$ of these pairs, such that for all $x_i, y_i$, a ...
0
votes
1answer
53 views

Recurrence relation question - check my answers! Basic questions.

I had a chat with a friend about these questions (they are homework questions) , and we argued about the solution. I would just like an outside opinion about my answers: 1) $n \geq 2$ people are ...
0
votes
1answer
70 views

Recurrence relation - simple question. Homework. Permutations with a twist,

I think I solved it but I would love someone to tell me if I'm wrong. the question is as follows: $n$ people are sitting on a bench with $n$ seats. Find a recursive equation that calculates how many ...
0
votes
1answer
32 views

Permutation and combination.

In how many ways can 12 indistinguishable apples and 1 orange be distributed among 3 distinguishable children in such a way that each child gets at least one fruit? What if the apples are different ...
1
vote
1answer
290 views

In a standard deck of 52 cards, how many different 7 card hands are there in which 3 cards are hearts and the other 4 are of different suits?

I know there are 13 cards in each suit, so that would mean I needed 3 of the 13 hearts or 13 P 3, then the other 4 would need to be out of 39 so it would be 39 P 4 but I don't know where to go from ...
3
votes
2answers
67 views

combinatorics - fixed point permutations

Simple question but I just need a little tip to finish it. we are given $A=\{1,2,3...,2n-1,2n\}$ the set of all integers between and including $1$ and $2n$. We are asked how many different ...
0
votes
1answer
19 views

Permutation combination questions?

An access pad has 7 buttons. An access code is a sequence of 2, 3, 4 buttons. How many access codes are possible if: buttons may be repeated buttons may not be repeated I need help getting this ...
2
votes
1answer
55 views

Finding probability of earning points

A professor asks a true/false question with ten individual questions. Suppose the professor assigns grades of: $10$ points for each correct response, $0$ points for each absent response, and $-10$ for ...
0
votes
0answers
29 views

Bijection inequality

Suppose $a$,$b \in \mathbb{R}^n$ are such that $$0 \leq a_1 + \leq a_2 + \cdots + \leq a_n $$ and $$0 \leq b_1 + \leq b_2 + \cdots + \leq b_n $$ If $\sigma : \{1,2,3,\ldots,n\} \rightarrow ...
2
votes
2answers
72 views

Find the number of permutations in $S_n$ containing fixed elements in one cycle

Find the number of permutations in $S_n$ such as 1 and 2 belong to one cycle.
1
vote
1answer
72 views

Permutation and combination of letters

I need help with the following question: "Given that a computer can only type letters A,B,C,D and E, how many ways can I type in 6 letters such that they must contain at least all of the different ...
2
votes
2answers
68 views

Prove that $S_n$ satisfies the following property: if $g \in S_n$, then $g$ and $g^{-1}$ are conjugate in $S_n$.

So I tried setting up an arbitrary $g$ such that $g(a_1)=b_1, ... g(a_k)=b_k$, and then I fizzled out. So I'm showing that for every a in $S_n,\ ag(a^{-1}) = g^{-1}$. I'm showing that they have the ...
2
votes
2answers
122 views

Coefficient of $x^n$

What is the coefficient of $x^n$ of this following expression: $$(x+x^2+x^3+ \dots + x^r)^n$$ I tried it but failed. I know that it can be solved by combinations but ...
0
votes
3answers
46 views

Counting more strings with 7 letter

Already made one sort of like this earlier (Counting strings with 7 letters), but I'm still not getting into the mindset required for this kind of tasks. Anyway, I'm given the letters A-G and.. I ...
0
votes
1answer
68 views

Mississippi Problem Need Help

Please help me to solve this: How many permutation & combination can be be formed from the word $MISSISSIPPI$ taking $5$ at a time?
0
votes
2answers
109 views

How many triangles can be made with those holes?

A 5 by 5 square lattice is formed by drilling holes in a piece of wood. Three pegs are placed in this lattice at random. Find the probability that three randomly chosen points of a 5 by 5 lattice ...
1
vote
1answer
54 views

Find The Number Equation Solutions

Find the number of non-negative integer solution of the equation: $$5x_{1}+x_{2}+x_{3}+x_{4}+x_{5}=14$$
0
votes
1answer
131 views

Permutations and symmetric groups

Suppose that a permutation $f$ is the product of disjoint cycles $f_1,f_2,\dots, f_m$. Show that $o(f)$ is the least common multiple of $o(f_1), o(f_2),\dots, o(f_m)$. Really lost with the question.. ...
1
vote
0answers
122 views

Magic Square Combinatorics

This question has been noted to be close to a Project Euler question. Please Help me with this question:Considering a 4*4 magic square ,How many ways are there to fill each square with an integer ...
0
votes
1answer
56 views

Communicating with Language

Can you please help me with this problem? There are $n$ people living on a planet. It is known that their planet has $6$ languages and each person knows every language. It is also known that any two ...
1
vote
1answer
48 views

Orders of Cycles

Suppose $\tau$ is a cycle of order $n$. I am trying to show that $\tau^k$ is a cycle if and only if $\gcd(n,k)=1$. $\Rightarrow$ If $\gcd(n,k)=1$, then the order of $\tau^k$ is $n/\gcd(n,k)=n/1=n$. ...
1
vote
0answers
30 views

Count possible decodings for given number

If A = 1, B = 2, C = 3,....,Z = 26 How to count possible decoding for given any integer number? EXAMPLE : NUMBER : 111 --> ANSWER : 3 EXPLANATION : ...
2
votes
2answers
202 views

Difference of number of cycles of even and odd permutations

Show that the difference of the number of cycles of even and odd permutations is $(-1)^n (n-2)!$, using a bijective mapping (combinatorial proof). Suppose to convert a permutation from odd to even we ...
0
votes
1answer
53 views

Permutations Question: Letter Arrangements with Restrictions

How many arrangements can be made of the letters in the word PHOTOGRAPH? What I did was, $8P5$ to find the number of arrangements between the two H's, then multiplied by 4! because the 5 letters and ...
1
vote
2answers
23 views

Combinations Question?

In how many ways can 6 different books be distributed between 2 students, provided that both students receive at least one book? Thanks for helping
0
votes
3answers
244 views

Selecting a committe with two women refusing to sit together.

In how many ways can a committee of $3$ women and $4$ men be chosen from $8$ women and $7$ men if two particular women refuse to serve on the committee together? I've approached this question by ...
1
vote
2answers
127 views

Nine digit sequences with exactly one zero, two ones, three twos

I'm working on a problem where I am to find the number of nine digit sequences when there are exactly one zero, two ones and three twos. I worked up a solution, but is it correct? Here's my line of ...