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

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0
votes
2answers
45 views

How many hands are there with exactly 5 hearts after drawing 7 cards from a deck? [on hold]

Draw 7 cards from a deck of 52 cards. How many hands are there with exactly 5 hearts? Will it be something like $$\frac{1!}{(52!51!50!49!48!)\cdot(7!6!5!4!3!)}$$ I'm pretty sure its wrong, any help ...
2
votes
5answers
825 views

Number of mixed doubles pairs such that no one plays with his/her spouse?

Can you help me with this problem? There are $7$ married couples. What will be the number of mixed double pairs in tennis such that no one plays with his/her spouse? Can some one help me with ...
0
votes
1answer
24 views

Using Maple, to calculate how many times does the digit 7 occur in the numbers from 1221 up to 12021? [on hold]

I need to write a program in Maple to calculate how many times does the digit 7 occur in the numbers from 1221 up to 12021? Please help. Thanks.
0
votes
1answer
29 views

How many ways can we put $5$ red balls, $4$ green balls and $3$ white balls into $12$ slots?

How many ways can we put $5$ red balls, $4$ green balls and $3$ white balls into $12$ slots? Would it be $12!$ or $\dfrac{12!}{5!4!3!}$? I'm confused here.
-2
votes
0answers
30 views

Permutation/Combination Question!

A club is forming a committee to plan its annual Holiday Dance. One person will serve as Chair of the committee, another will be Vice-Chair and there will be two other members. Is this an example of a ...
2
votes
0answers
33 views

Permutation & combination for creating housie tickets

A game called housie (similar to Bingo) is played in India. This game is played by a group of people based on a few rules. I need to know how many unique tickets can be printed in one session of a ...
0
votes
1answer
28 views

Problem finding the number of r-element multi-subsets of the multi-set $M=\{ a_{1},a_{2},…,a_{n},m.b \} $

Let $m,n,r \in \mathbb{N}$. Find the number of $r$-element multi-subsets of the multi-set $$M= \{ a_{1},a_{2},...,a_{n},m.b \} $$ when $r \leq m,r\leq n$. Below is the given answer. ...
0
votes
0answers
37 views

How many Possible Combinations exist?

I have $120$ coins and $21$ buckets. Each bucket can hold $0$ to $20$ coins. How many possible coin/bucket combinations are there?
0
votes
2answers
27 views

Proving $ \sum_{r=0}^{n} \frac{1}{r+1} \binom{n}{r} = \frac{1}{n+1} (2^{n+1} - 1) $

I'm stuck at proving the following. $$ \sum_{r=0}^{n} \frac{1}{r+1} \binom{n}{r} = \frac{1}{n+1} (2^{n+1} - 1) $$ This is what I have so far. $ \sum_{r=0}^{n} \frac{1}{r+1} \binom{n}{r} = (1) ...
4
votes
1answer
236 views

$N^\text{th}$ (in lexicographical order) term of balanced brackets string

We have the following balanced brackets permutations of length $4\cdot2$ in lexicographical order: ...
1
vote
2answers
30 views

Probability of being selected twice in a week given a set of n people?

Let's say a child is selected out of a group of 10 students each day to stay after school and help clean the classroom. What is the probability that a particular child is selected exactly twice during ...
0
votes
1answer
11 views

number of rectangles (including squares)

I have a grid of squares of unit length each with value 0 or 1. I want to count the number of squares or rectangles that can be made within this grid no taking the unit sqaures with value 1. If the ...
1
vote
1answer
15 views

How many words can be formed by taking 4 letters at a time from the letters of the word 'MORADABAD'?

What I tried was: (9P4)/3!*2! This gave me a wrong answer (since the answer is 626). I'm unable to make use of the hint provided in my book: "make cases". Any help would be appreciated. :)
0
votes
0answers
13 views

count the permutation which have $k$ maxima

I need some help for the following homework question. A permutation $P (\pi_1\pi_2...\pi_n)$ of {$1,2,...,n$} is given. We say that $j$ is a maxima of $P$ whenever $\pi_j$>$j$. How can I find ...
1
vote
3answers
63 views

Problem proving $ P_{r}^{r} + P_{r}^{r+1} + … + P_{r}^{2r} = P_{r}^{2r+1} $

Show that $$ P_{r}^{r} + P_{r}^{r+1} + ... + P_{r}^{2r} = P_{r}^{2r+1} $$ where r is a nonnegative integer. This is what I've come up with so far but I'm not sure how to continue. I know I need to ...
0
votes
0answers
13 views

arrangement with inclusion-exclusion

How to solve the following problem using inclusion -exclusion principle? Given n and a letter C,how many possible words of length n can be formed that are with no two consecutive C in the word. For ...
1
vote
0answers
13 views

The number of ways to schedule six activities

I'm trying to review for Probabilities and Statistics and came upon this Question. If one needs to schedule a job interview for someone who wants to teach at a school. For the day of the interview, I ...
0
votes
0answers
15 views

Combinatorics or permutations of language? [on hold]

I am looking to understand the combinatorial or permutative space of the English language. 26 letters up to length 25. How big is the space? And if anyone has an algorithm for this in shell or ...
0
votes
1answer
18 views

arrangement with condition

Given n and a letter C,how many possible words of length n can be formed that are with no two consecutive C in the word. For example,if n=3, C='b',then the word bcb,ccc,aab do not have any ...
18
votes
6answers
17k views

Combination of smartphones' pattern password

Have you ever seen this interface? Nowadays, it is used for locking smartphones. If you haven't, here is a short video on it. The rules for creating a pattern is as follows. We must use ...
2
votes
1answer
28 views

Algebra - proof verification involving permutation matrices

Theorem. Let $\textbf{P}$ be a permutation matrix corresponding to the permutation $\rho:\{1,2,\dots,n\}\to\{1,2,\dots,n\}$. Then $\textbf{P}^t=\textbf{P}^{-1}.$ Proof. First note the following ...
1
vote
1answer
28 views

Cycles of odd length: $\alpha^2=\beta^2 \implies \alpha=\beta$

Let $\alpha$ and $\beta$ be cycles of odd length (not disjoint). Prove that if $\alpha^2=\beta^2$, then $\alpha=\beta$. I need advice on how to approach this. I recognized that $\alpha,\beta$ are ...
0
votes
1answer
28 views

Solving an equation involving factorial notation

I was given this problem in the text book: $$\frac{(n+4)!}{(n+2)!} = 6$$ $$n \in I $$ Since the textbook doesn't have the solution, I'm wondering if I'm right: $$\frac{(n+4)!}{(n+2)!} \Rightarrow ...
0
votes
0answers
31 views

How to compute the topological entropy of a permutation?

I have a permutation, say as ${4,1,7,2,3,5,6}$, given by its induced matrix. According to this paper (Proposition 11 on p. 82), To compute its topological entropy, one can compute the ...
0
votes
1answer
11 views

String Permutation

If we have the string ab, would abab be a permutation of ab? It seems that a permutation is a rearrangement of things but only within the things in our set. In this example, that set is ab.
0
votes
0answers
60 views

What combination of the 16 listed digits make two numbers N and M that fit in the equation M=2*N

Here's the whole problem: Consider the list of 16 digits 2; 2; 3; 3; 4; 4; 5; 5; 6; 6; 7; 7; 8; 8; 9; 9: Can these digits be used as the digits of two numbers, M and N, with M = 2N? If yes, produce ...
1
vote
0answers
16 views

Total number of possible graphs in a network with $m$ edges and $n$ vertices?

How do you calculate the total number of possible graphs in a network with $m$ undirected edges and $n$ vertices? No self-loops. For instance, if I have a network with $7$ vertices in it, I want to ...
10
votes
0answers
324 views

Sorting of prime gaps

Let $g_n $ be the $n^{th}$ prime gap $p_{n+1}-p_n.$ If we re-arrange the sequence $ (g_n)$ so that for any finite $n$ the gaps are arranged from smallest to largest we have a new sequence ...
0
votes
3answers
53 views

Need help with flaws in statistical reasoning

The problem is as follows - there are three couples and six chairs in a row. The six individuals are seated at random. What is the chance that at least one couple will be seated together? Here's my ...
0
votes
1answer
27 views

permutations and combinations very tough

In how many ways can the letters of the word 'arrange' be arranged if the two r's and the two a's do not occour together?
0
votes
0answers
34 views

Distributing balls in boxes.

In how many ways can $n$ identical balls be distributed amongst $m$ different boxes given that a box can have any number of balls(from $0$ to $n$)? What I've tried is using multinomial theorem to ...
0
votes
1answer
137 views

Is the permutation $\alpha : \mathbb Z_{11} \rightarrow \mathbb Z_{11}$ given by $\alpha(x)=4x^2-3x^7$ a cycle or not?

The permutation $\alpha : \mathbb Z_{11} \rightarrow \mathbb Z_{11}$ given by $\alpha(x)=4x^2-3x^7$ is a cycle? If it´s not a cycle then write it as a product of disjoint cycles.
2
votes
2answers
491 views

How many 90 ball bingo cards are there?

In the UK there are 90 bingo balls. A bingo card consists of 9 columns and 3 rows. A row contains exactly five numbers and four blanks. A column consists of one, two or three numbers and never three ...
0
votes
1answer
26 views

Permutation with atleast n unique characters

I came across this question on Google APAC 2015. I am slightly weak with permutations. The problem goes like this: There is a password. We know the length of the password and the characters used ...
2
votes
2answers
103 views

Hat Matching Problem Expectation

I have an interesting problem in the context of the hat matching problem: There are n people with hats at a party. Each person randomly grabs a hat. A match occurs if a person gets his own hat. I'd ...
0
votes
2answers
23 views

Stuck with divisibility test in Permutations

How many 5 digit numbers can be formed using digits 0 to 7, divisible by 4, if no digit occurs more than once in a number. 1480 780 1360 1240 None Of These I could calculate the ...
2
votes
2answers
70 views

How many ingredients does he use if the burger has 99 varieties?

A burger-shop keeper says that he has 99 varieties. My questions is: how is it possible to have 99 varieties? How many ingredient does he uses? I am saying this because there is no number, whose ...
1
vote
2answers
25 views

Permutation and Combination for 6-digit numbers contain exactly 4 different digits

I found a question online. How many 6-digit numbers contain exactly 4 different digits ? My Solution is : There are 6 digits and 4 needs to be unique so either 2 digits can be same or 3 can be same. ...
0
votes
0answers
11 views

Number of Different Combination Possible?

You are given number of places as m and number of digits as n.You have to fill those m places in such a way that each digit appears atleast one time. For Example Given m as 4 and n as 3 so you have ...
0
votes
1answer
37 views

How many n-digit numbers can be formed using x single digit numbers? [closed]

For instance, I have to form 4 digit numbers with the any 3 digits, say 1, 2 and 3. There are several possible numbers that can be formed by arranging these digits in various orders, but I am unable ...
0
votes
0answers
27 views

How many sequences can be generated? [on hold]

Given $m$ distinct letters. How many unique patterns of size $n$ can be generated using the $m$ letters such that every letter occurs at least once? Given: $n$ $>=$ $m$
1
vote
2answers
29 views

Order of a permutation

What does the order of a permutation actually mean? I accept the fact that it is the l.c.m. of the lengths of the cycles in its cycle decomposition, but I don't really have an intuition for what the ...
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
2answers
260 views

Permutation and combination problem - word arrangement

This is a question of permutation and combination. Q. How many words can be formed from the word "LUCKNOW" when i) No restriction is there ii) L is the first letter of the word iii) All the ...
2
votes
1answer
31 views

Possible number of arrangement.

Question: How many cars are there with number GJ-X-AB-abcd. GJ and A are constant.X is digit between 1 to 9, B is english alphabet and abcd is 4 digit number.(a can be zero) My Efforts: It is but ...
0
votes
0answers
18 views

How many arrangements (correct and incorrect) possible with cube puzzle pieces in a particular unfolded form?

I am trying to do a computer program for arranging cube puzzle pieces in an unfolded form. A cube can be unfolded into 11 forms or nets. I have chosen a single net for now for simplicity purposes and ...
1
vote
2answers
22 views

Permutations and Sample Spaces

Suppose 3 cars can either turn left $(L)$, turn right $(R)$, or go straight $(S)$. I need to find the sample space for all the possibilities but I am not sure how to do that. I know that for 3 cars ...
-1
votes
3answers
27 views

How many distinct permutations can be made from the letters of the word IN F IN IT Y? [closed]

How can I determine how many distinct permutations can be made from the letters of the word infinity ?
0
votes
0answers
14 views

Cyclic Permutation of identical objects

I just want to confirm if this formula for cyclic permutation of identical objects is correct. If there are n objects of which p are identical of one kind, q are identical of second kind, r are ...
0
votes
1answer
32 views

A Question on distribution numbers

This is a question from the book Combinatorics -a problem oriented approach which states: Q.1 Find the no. of distributions of a set of distinct balls into a set of distinct boxes, if no boxes can ...