0
votes
1answer
32 views

Could someone help me out with permutations/combinations?

I need some help understanding how to approach problems with permutations/combinations. Could someone first explain when I should be using combinations and when I should be using permutations? Then ...
0
votes
1answer
8 views

Permutation question in discrete mathematics. At least 1 out 3 members (P) from a total of 10 members

Im doing a question out of Discrete and Combinatorial mathematics by Grimaldi (4th Edition). Im stuck on one of the questions and am trying to find an alternative way of doing it, that is not in the ...
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vote
1answer
20 views

Verify my thought process on permutations

If there are $15$ distinguishable objects; all will be placed into $2$ boxes. There needs to be at least one object in each box. How many ways can you place these objects into the $2$ boxes? Tried ...
0
votes
2answers
24 views

Permutation and combination related question

My question is: Starting from Washington, DC, how many ways can you visit 5 of 50 state capitals and return to Washington? I tried to solve it, Firstly, we should choose 5 states from 50 countries ...
0
votes
1answer
20 views

What are the total number of ordered permutations of a list of elements (possibly repeated)?

This question is a part of a TopCoder problem. I am learning algorithms, and just got stuck at this (not homework). Suppose we have a set $A$ of integer elements, such that $n(A) = a$ (number of ...
1
vote
2answers
27 views

Why does the wording of how many ways can a photographer 6 people from a group of 10 ask for permutations and not combinations?

Note: Please do not post the mathematical notation for binomial coefficient or "n choose m" or anything related to that. The chapter where that is introduced comes much later. Therefore I would not ...
0
votes
1answer
15 views

Find the possible number of assignments?

S students, I interviewers, each student has to undergo R interviews, each interviewer can interview at max X students. No student interviews with an interviewer more than once, and no interviewer ...
0
votes
1answer
21 views

Basis Composition of permutations

Hi I have the following questions: Calculate the following compositions of permutations on $A=\{0,1,2,3\}$ $(12)(102)$ Ans:$(02)$ $(01)(23)(0123)$ Ans:$(02)$ $(123)(32)$ Ans:$(13)$ ...
3
votes
3answers
40 views

Number of $r$ letter words taking letters from a $n$ letter word

I can't figure out how to do questions such as this one, any thoughts? What is the number of four letter words that can be formed from the letters in BUBBLE ...
0
votes
2answers
31 views

Ways to award first and second place to two persons out of nine

Question: In how many ways can the first and second place be awarded to two persons from among 9 people. ...
1
vote
1answer
48 views

Prove by Structural induction, circular permutations

Prove by Structural Induction: For a circular permutation of $n$ elements, the number of permutations is $(n-1)!$ How is this done?
1
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0answers
36 views

Color Cyclic Permutations

Suppose there are n people sitting in a circle,wearing 3 kind of shirts viz. white,red and green. When two people with different shirt color talk with each other, they both change their shirt to ...
1
vote
3answers
35 views

Problematic Permutation Problem

i see a problem without any definition. would you please help me? i want to calculate the number of permutations of 1,2,...,1392 that 696 numbers be in the natural positions (from all numbers, 696 ...
1
vote
3answers
73 views

Counting valid tickets

I think my question is very easy but I need to understand. The problem is, I have a ticket with 2 numbers from 1 to 10. The first number cannot be greather than the second number. How many valid ...
1
vote
1answer
44 views

Determining the different number of subsets (counting, permutations, combinations)

Given that any fixed integer n>0, let S={1,2,3,4,...,n}. Now a Red-Blue subset of S is called T. Every element of T is given a colour (either red or blue). For instance {17 (red)}, {1 (red), 5(red)} ...
1
vote
1answer
52 views

Permutations, Combinations, and Counting

A group of 63 people are camping together. They have two 6-person tents, three 4-person tents, five 3-person tents, and three 2 person tents. 18 people will sleep outside of the tents under a tarp. ...
4
votes
2answers
107 views

Count Number of Sequences

The question is: Given a sequence of positive integers A={1,2,3,...,N}. Count the number of sequences you can get after making K swaps between adjacent element on it for a given N ? My approach: My ...
0
votes
3answers
32 views

DNA Sequence Distinct Way

we know The genetic code is based on the four nucleotides adenine (A), cytosine (C), guanine (G), and thymine (T). These are connected in long strings to form DNA molecule. with three A, one C, two G ...
1
vote
1answer
38 views

Prove summation related to cycles

Let $b_r(n,k)$ be the number of n-permutations with $k$ cycles, in which numbers $1,2,\dots,r$ are in one cycle. Prove that for $n \geq r $ there is: $$ \sum_{k=1}^{n} ...
2
votes
1answer
37 views

Find the permutation

This is part of an exercise I did on an assignment but I am having trouble remembering how to complete the exercise (even though I got full marks on my assignment). Let $P_1=(3\,4\,1\,2\,5), ...
1
vote
2answers
60 views

Fill $8$ boxes with $60$ items

I have $8$ boxes and $60$ items: how many ways can I fill the boxes so that The order of the items in each box does not matter It does not matter which boxes are filled with which items. In other ...
0
votes
1answer
38 views

Permutations Discrete Math

Roll a standard die n times. For finding the number of permutations of getting exactly k 3's you would do ${n\choose k} \cdot {5} ^{n-k} $ But what about finding at least k 3's? I was thinking of ...
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vote
1answer
48 views

Basic combinatorics question, can you help me?

Before I start let me thank anyone that contributes to helping me with an answer for this. Ok - on to the question. Assume you have 10 jelly beans, 5 yellow and 5 red. What is the total amount of ...
0
votes
1answer
17 views

Count the number of mixes of the card to get come back to origin

Mix a deck of 52 cards by placing them in two parts and take alternate cards from both stacks. Use the cycle notation to show that it only takes 8 mixes to come back to the origin. Since we want ...
0
votes
2answers
38 views

Discrete Math- Counting [closed]

I'm trying to answer this question for my discrete homework.Any help would be appreciated. Find the number of subsets of $S=\{1,2,3,4,5,6,7,8,9,10\}$ that contain exactly five elements, including ...
1
vote
1answer
45 views

Permutation + Combination

this is a question I had on my midterm, and I can't seem to be sure what the answer is and our professor did not post the solutions, therefore I cannot make sure I got it right (or wrong). How many ...
2
votes
1answer
27 views

In how many ways can letters in mathematics be ordered with restrictions?

I've been stuck on these for a while. Please guide me through all the steps because I actually want to understand this. I've got an exam coming up. Consider the letters in the word "MATHEMATICS". In ...
0
votes
1answer
34 views

How many way can 7 friends line up if there are certain conditions?

How many ways can 7 friends line up if Ann, Beth, and Chris have to stand next to each other where Ann is ahead of Beth and Beth is ahead of Chris? Would it simply be $5*4*3*2*1=120$ ways? Expanding ...
3
votes
0answers
25 views

(Counting problem) more challenging Modular N algebraic eqs - for combinatorics-permutation experts

Experts in algebra please help - Part II after Part I: we would like to know the number of solutions for this set of six of modular N algebraic equations: $$ x_1 y_2 = x_2 y_1 \pmod N \qquad (1) \\ ...
2
votes
1answer
80 views

How many ways can six of the letters of the word ALGORITHM be selected and written in a row if the first letter must be A?

As the title states, the question is: "How many ways can six of the letters of the word ALGORITHM be selected and written in a row if the first letter must be A?" I don't really get what the problem ...
3
votes
3answers
329 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
49 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: ...
4
votes
1answer
81 views

Can someone please clarify combinations vs permutations?

I see similar questions asked on here and obviously I did some research and read my book, but it seems like every explanation contradicts another in some way. There are basically infinite scenarios ...
0
votes
1answer
53 views

What's the difference between a permutation and a combination with repetition?

My understanding is that a permutation is used to find the number of rearrangements of different elements, taking into account possible orders. A combination is used to find the number of ...
1
vote
1answer
130 views

In how many ways can you arrange the alphabet so that A and B are always next to one another (In either order)

Ok, so I have no idea where to begin on this question. Do I treat A and B as one letter? 25 choose n?
1
vote
1answer
36 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 ...
1
vote
0answers
51 views

I want to generate(or count) all possible binary matrix that satisfy certain Condition

I want to generate(or count) all possible binary matrix that satisfy below Condition. let A be arbitrary binary matrix 4*4 ...
2
votes
1answer
71 views

How many positive integers n can we make with the digits 3, 3, 4, 5, 5, 6, 7, if the number n > 4, 000, 000?

According to my study guide the answer to the exercise, How many positive integers, (n), can we make with the digits 3, 3, 4, 5, 5, 6, 7, if the number n > 4, 000, 000, : The total of numbers n > ...
0
votes
1answer
51 views

How many different 5 characters words are there with only one letter a?

I just need to clarify my answer to this exercise. This is a permutations exercise. If we define a word to be a string of 5 letters of the English alphabet, regardless of meaning, then mnnnw is a ...
0
votes
3answers
551 views

A bowl contains 10 red balls and 10 blue balls, A women selects ball at random without looking?

How can we solve this question ? A bowl contains $10$ red balls and $10$ blue balls, and a women picks up balls from the bowl, at random, without looking. A) How many balls must she pickup in ...
0
votes
0answers
53 views

Using Binomial Theorem to show that (-1)^k C(n,k) [duplicate]

I came across this question on my text book and i didn't know how to prove it. Use the Binomial Theorem to show that $$ 0=\sum_{k=0}^n \ (-1)^ {k} C(n,k)$$
2
votes
3answers
131 views

Give a combinatorial argument to show that C(n,k) = C(n,n-k)

What is combinatorial argument and how can i prove this equation ? As far i understand i think we have to apply the Chu-Vandermonde identity but i am not sure if thats right or not. ...
4
votes
2answers
295 views

Expected Value of Local Maxima and Local Minima

Recently I came across this question: Given a random permutation of integers 1, 2, 3, …, n with a discrete, uniform distribution, find the expected number of local maxima. (A number is a local maxima ...
1
vote
2answers
56 views

Ways to select three-man teams

In a competition there are 18 competitors. Answer the following: A) During the first day they're competing in three-man teams (total of 6 teams). How many ways are there to select the teams? B) If ...
1
vote
2answers
158 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 ...
0
votes
1answer
109 views

proving bitstrings [duplicate]

1.Let it be $a_n$ the number of bitstrings which contain 000 How would I prove that for $n\ge4$: $$a_n = a_{(n-1)} + a_{(n-2)} + a_{(n-3)} + 2^{n-3}$$
0
votes
2answers
89 views

Calculate product of transpositions

I've searched for this kind of question-answer, but didn't managed to find one because the problem is quite specific. Let me explain: I have permutation: $(13927)(5846)$ which I must write as ...
1
vote
5answers
222 views

How many permutations of {1,2,…, 9} are there that do not start or end with an even number?

How many permutations of $$1,2,..., 9$$ are there that do not start or end with an even number? This is my attempt Condition 1 [Starts with even] => $$4 * 8!$$ Condition 2 [Ends with even] => $$4 * ...
1
vote
3answers
68 views

Permutations for paths

What is the counting sequence for paths from $$(0,0)\text{ to }(n,n)$$ where $$2n$$ is the size of the path (number of steps) and n can vary over all nonnegative integers. I don't know how to ...
1
vote
1answer
27 views

Number of orders and combinations

I have just done these two questions and I have answers for them but I am not sure if they are correct. A jazz band is to give one concert in each of nine selected cities. Calculate the total ...