# Tagged Questions

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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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: ...
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: ...
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 ...
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 ...
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 ...
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 ...
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? ...
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?
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 ...
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 ...
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 ...
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?
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 ...
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 : ...
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 ...
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: ...
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.
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
0answers
29 views

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 ...