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

learn more… | top users | synonyms

0
votes
2answers
26 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 ...
0
votes
0answers
16 views

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 ...
0
votes
1answer
25 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} * ...
-2
votes
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
1
vote
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 ...
0
votes
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 ...
3
votes
0answers
38 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
vote
1answer
27 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, ...
-3
votes
1answer
63 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
votes
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
0
votes
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 ...
0
votes
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
votes
2answers
45 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 ...
0
votes
3answers
28 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
votes
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
votes
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 ?
0
votes
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
votes
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 $ ( -)\\ (- -)\\ (- ...
0
votes
2answers
32 views
-4
votes
0answers
27 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 $\dbinom{n+1}{r-1} = (n-r-1) \dbinom{n}{r-1}$.
1
vote
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
votes
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 ...
0
votes
2answers
117 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
votes
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
votes
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
votes
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
votes
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
votes
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
vote
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
votes
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
votes
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 ...
-3
votes
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?
0
votes
0answers
11 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 ...
0
votes
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
votes
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? ...
1
vote
2answers
103 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 ...
1
vote
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
votes
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 ...
4
votes
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
votes
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 ...
0
votes
1answer
22 views

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

How many committees are possible? I added the total number of women ($17$) and the total number of men ($21$) to get $38$ total people. I used this as my $n$ or objects. I then subtracted my $r$ ...
2
votes
1answer
18 views

How many possible permutations are possible if ranking n entities using the 'standard competition ranking' strategy?

I don't know if I'm missing something here, but this doesn't look as straightforward to me as I thought it to be. I basically want to calculate the number of unique rankings that are possible when ...
4
votes
2answers
47 views

A sequence $a_i$ such that $|a_1-a_2|,|a_2-a_3|,\ldots$ is also permutation of the positive integers

Let $a_1,a_2,\ldots,$ be a permutation of the positive integers. Is it possible that $|a_1-a_2|,|a_2-a_3|,\ldots$ is also a permutation of the positive integer? My idea is to construct the sequence ...
1
vote
1answer
18 views

Arrange numbers to prove question

Prove that 100 0's, 100 1's, 100 2's, 100 3's, 100 4's, 100 5's, 100 6's, 100 7's, 100 8's and 100 9's cannot be used in any form to make a perfect square. I have no idea how to do this question. I ...
0
votes
1answer
29 views

Find all possible arrangements of numbers, but keeping the sum constant

How would I find all possible combinations of $n$ natural numbers from 1 to 100, in such a way the sum of the $n$ numbers is always 100. For example if $n = 3$, possible answers would be: $(1, 2, ...
0
votes
0answers
26 views

Possible choices for coloring boxes with exactly n colors

I have a number of boxes $N$ that I each need to paint with one color chosen from $n$ available colors. Every color must be used at least once and the order in which I color the boxes matters. For ...
0
votes
1answer
27 views

combinatorics four digits out of three

With three given digits (1,2,3), how many unique four-digit combinations can be made if all three digits must be present but may be repeated? Example of correct combinations: (1,2,3,3) (1,1,2,3) ...
0
votes
1answer
34 views

A combinatorial coefficient linked to exterior product

I am looking at the following sum $$ \sum c_1\wedge \cdots\wedge c_n $$ where the summation ranges over $c_1,\ldots,c_n$ such that each $c_i\in\{a,b\}$ and $a$ appears exactly $j$ times. Thus, using ...
1
vote
1answer
35 views

Permutation and combination difference, a flower shop question

I have got a perm/combination question In a certain flower shop, only 3 vases of flowers and 1 wreath can be displayed in the front window at a time. If there are 10 vases of flowers and 4 wreaths ...
-4
votes
3answers
73 views

How many positive integer are there ?? [closed]

My task is to calculate the number of positive integers which are smaller than 10000 and contain “1”. Please give me some hints; thanks in advance.