Combinations are subsets of a given size of a given finite set. All questions for this tag have to directly involve combinations; if instead the question is about binomial coefficients, use that tag.

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Permutation/Combination question on dice

Question: Three dice (six faces: each face -> number 1 to 6) are rolled. What is the number of possible outcomes such that at least one die shows number 2? My attempt: One die has to show two. ...
2
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0answers
18 views

What is the combination of Complex, Split-Complex and Dual Numbers

If $a+bi:i^2=-1$ is a complex number, $a+cj:j^2=+1$ is a split-complex number, and $a+d\epsilon:\epsilon^2=0$ is a dual number; what is the term for the combination ...
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2answers
49 views

How many 10-character strings can be formed using p characters [on hold]

Let $A = \{a_1, a_2, . . ., a_p\}$. In how many ways you can select 5 elements? Let $A = \{a_1, a_2, . . ., a_p\}$ is a set of $p$ symbols. In how many ways you can make codes consists of 10 symbols? ...
2
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4answers
66 views

How to find the number of possible outcomes of 10 games between 20 teams?

Hi I am looking for an equation to find possible combinations in a non repeating format with a twist. Here is the example: There are 10 games between 20 teams. I have to chose 5 winners but ...
4
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3answers
233 views

how many ways to choose 3 coins?

Sorry I don't know the correct math terms here, I haven't had a math class in some time. That's probably why I have trouble finding an existing question like this, too. Let's say there are 4 differnt ...
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1answer
33 views

Number combinations - website [on hold]

There are four directions: up, down, left, right. (I am programming something). Four patterns with one (up, down, left, right), 16 patterns with two (up up, up down, up left, up right) and so on. I ...
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1answer
14 views

combination and permutation SETS [on hold]

In a sports team, there are 5 grade 12 players, 4 grade 11 players, 3 grade 10 players. In how many way can a coach select a group of players if: a) There must be 2 or more players? b) There must ...
3
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3answers
233 views

Is there a closed-form formula for sum of “odd combinations”? [on hold]

So, I was trying to come with a formula for the sum of below series: ${2^n \choose 1}+{2^n \choose 3}+...+{2^n \choose 2^n - 1}$ Thank you.
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2answers
52 views

Stars and bars with minimum number of categories

I've been trying to figure out a closed form solution to this problem, but I haven't been able to find one yet. How many ways are there to pick $n$ items from $k$ categories, such that at least ...
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0answers
38 views

Distinguishable balls in distinguishable boxes?

Suppose I have $n$ distinguishable balls and $N$ distinguishable boxes. A particular configuration of this 'system' is such that there are $k$ particles in a box, b, where $1\lt b \lt N$ (i.e. the ...
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2answers
45 views

Scores of six soccer matches

In the first round of the city soccer tournament, the teams in group A finished as follows: ...
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3answers
56 views

Let $A=\{0,1\}$. How many strings of length $5$ are in $A^*$ where at least two $1$ are next to each other?

Let $A=\{0,1\}$. How many strings of length $5$ where at least two $1$ next to each other are there in $A^*$?
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1answer
15 views

No. of ways to shuffle a card

How many ways are there to shuffle N cards such that exactly one card is in the same position?(Assuming that initially the card no. 1 is in the first position,card no.2 is in the second position and ...
1
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4answers
19 views

Prove by combinatorial argument.

$$ \binom{n}{r} \binom{r}{k}=\binom{n}{k}\binom{n-k}{r-k} $$ I was proving this equation, First i took L.H.S, then i open them with the help of Combinatorial Formula but, now I am Stuck, What to do ...
0
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2answers
24 views

combinations of 10 objects - of which 3 are distinct [on hold]

I need to count all possible combinations of a, b and c. There are 10 positions. Possible arrangements are: aaaaaaaaaa or aaaaaaaabb or aaaaaabbcc Permutations doesn't count twice: aaaaabbbbb == ...
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0answers
33 views

Difference between two expressions for combinations with repetition.

While attempting to solve problems that compute the number of combinations with repetition (ie, a store has 4 flavors of ice cream and you are picking 3 with repetitions allowed, how many ways can you ...
2
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0answers
97 views

Beads on the circle [duplicate]

It is placed the $n$ beads on a circle, $n \geq 3$. They numbered in random order. They are viewed clockwise. Beads for which the number of the previous bead less than the number of a next bead, are ...
2
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1answer
43 views

Counting the ways to color $k$ marbles blue in the circle with $m$ red marbles such that no neighbouring blue marbles

Let $m$ be a positive integer. The numbers $1,2, \cdots , m$ are evenly spaced around a circle. A red marble is placed next to each number. The marbles are indistinguishable. Adrian wants to choose ...
0
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2answers
61 views

Sum of the product of two combinations

Could anyone explain how this statement is true? You may notice that this statement is part of the process of adding two independent binomial r.v.'s. $$ \ \sum_{x=0}^\infty{n \choose x}{m \choose ...
4
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3answers
111 views

A question in permutation

Help is needed in solving the following problem. $8$ persons ($A$ and $B$ and $P, Q, R, S, T, U$) are to be seated in $2$ rows ($4$ seats per row). Find the number of ways that $A$ and $B$ are ...
1
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1answer
37 views

Equation for a systematic permutation

A $6$ digit number is set whereby every digit can be repeated without any constraints. So one can have a number between $000001$ and $999999$. (Zeros on the left are counted). The problem: Generate ...
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1answer
38 views

Five digit numbers where each digit can appear up to three times

The question is to determine how many five-digit numbers there are (using the digits 0-9) where each digit can appear up to three times in the number. The total number of numbers that can be made ...
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2answers
53 views

combination problem gre @

On the new years Eve , every member of a community exchanged cards with every other member. if a total of 420 different cards were exchanged , then how many different members were there in the ...
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0answers
39 views

Generating a random combination in O(k)?

I need to generate a "fair" random combination of $k$ items chosen from $n$ choices. All the algorithms I've been able to find so far (reservoir sampling, Fisher-Yates shuffle, ...) are of $O(n)$ ...
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2answers
52 views

Combinatorics: Participants in a match

In a tournament, each of the $6$ participants played 2 matches against each of the other participants. What was the total number of matches played during the tournament? So we have a set of 6 ...
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1answer
39 views

$t(n,r)$ ways of arranging $n-$ objects around $r$ circles

Consider the following combinatorial problem: Given $r,n\in \mathbb Z$ with $0\lt r\leq n.$ Let $t(n,r)$ denote the number of ways of arranging $n-$distinct objects around $r$ (indistinguishable) ...
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1answer
24 views

Permutation and Combination - Algorithm

Given Data in the problem For I= 1 to 10 print(x) means executing the immediate next line after for loop command 10 times. So here it prints "x" 10 times. Typical simple for loop construct in ...
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1answer
106 views

Loonies and Toonies Combinatorics

How many ways can you make $n$ Canadian dollars using only loonies (Canadian \$1 coins) and toonies (Canadian \$2 coins) such that the numbers of loonies and toonies are different from one another? I ...
-2
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1answer
51 views

Combination problem: random selection in a group

A scientific committee of 4 persons is to be randomly selected from a group consisting of 3 biologists, 3 physicists and 4 mathematicians. Let X denote the number of biologists, Y the number of ...
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0answers
18 views

factorial division word problem

I'm having some problems understanding the following: There are 3 programs being observed 4 times (total of 12 observations). There are 12 people used to investigate these programs, such that they ...
2
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2answers
55 views

Number of ways to enter 1,2,3,4,5,6 on the spots marked on three intersecting circles and have the sums of 14

How to solve it , i applied so many method but i could not find right answer, suggest me some method combination question gre 44
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2answers
20 views

Possible combinations [closed]

I'm trying to write a set of documents on LAMP (Linux, Apache, MySQL & PHP). In this series I have 11 Centos Versions, 3 Apache versions, 5 MySQL Versions & 9 PHP versions. I will be writing ...
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1answer
45 views

Find a Recurrence Relation

I want to find a recurrence relation for number of decimal numbers with length n, (we called $a_0$ ) that not includes 0 and any combination of 11,12, 21. i see the result is: ...
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1answer
57 views

Number of answers of equation amongs odd natural numbers

How many answer The following Equation has, in set of odd natural numbers? $x_1+x_2+...+x_k=n$, $k \equiv^2 n$ Solution: Comb ( [(n+k)/2]-1, k-1), comb means combination. how we get this?
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1answer
34 views

Number of different vectors.

Let's say that I have a vector with 6 elements. I put two wedges in the vector, i.e., at position 2 and position 6, for instance. And when I say put a wedge, it means... for every time you traverse ...
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2answers
42 views

Number of ways to split 10 items into groups of 5 and 3 and 2

There are 10 people, you want to split them into groups of 5 and 3 and 2. How many combinations are there? I am wondering if the ordering in which you choose the groups matters. For example if I pick ...
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2answers
31 views

Combination problem with distributing

I've been trying to do last exercise, but I can't figure out method to solve it. I read a book and searched for it in the internet, but I couldn't find exactly what I am looking for. Could you guys ...
0
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3answers
117 views

how many 4 digit numbers are there with 3 distinct digits, using all 3 of them.

My question is, if I have for example digits {1,2,3}, how many 4 digit numbers can I obtain if I have to use all of them in each combination? Correct combinations: {1,1,2,3} {1,1,3,2} {3,2,1,2} ...
0
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1answer
67 views

Number of ways to make n digit number?

Given M digits which are between 1 to 9, Find the number of ways to form N digit number, by repeating one or more given digits such that each of M digits are present in N digit number at least once. ...
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2answers
47 views

Discrete Math problem combinations and restrictions

I am trying to get my head around an idea but I can't seem to get it to work. Imagine you have the word "MAMMAL" Lets see I wanted to figure out how many ways I could rearrange the letters. Well ...
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4answers
30 views

no. of monomials in variables $w,x,y,\ldots,z$ of degree $m$

The formula for no. of monomials in variables $w,x,y,\ldots,z$ of degree $m$,$\,\,\,\,\,$ (where e.g. $x^iy^jz^k$ degree $m=i+j+k$) is: $\,\,\,\,\,$$\binom{m+n-1}{n-1}$ where $m$ is degree of ...
0
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1answer
51 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 ...
1
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2answers
84 views

Present a combinatorial argument for the identiy $\sum^{n}_{k=1} k\binom{n}{k} = n\cdot 2^{n-1}$

This is a question in my textbook that does not provide a solution. Any help on a solution? Consider the following identity: $\sum^{n}_{k=1} k\binom{n}{k} = n\cdot 2^{n-1}$ Present a combinatorial ...
0
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1answer
15 views

Is my interpretation about this problem on permutation and combination is correct - exactly 3 invitee?

A man has 9 frinds : 4 boys and 5 girls. In how many ways can he invite them, if there have to be exactly 3 girls in the invitees? ...
2
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2answers
142 views

Number of lattice paths

In my notes I have this: A lattice path is path consisting of step points $(x_0,y_0),(x_1,y_1),\ldots,(x_m,y_m).$ where either $x_{i+1}=x_{i}$ and $y_{i+1}=y_i+1$ or $x_{i+1}=x_{i}+1$ and ...
0
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3answers
48 views

How to solve this combination problem quickly?

In how many ways can 3 men and their wives be made stand in a line such that none of the 3 men stand in a position that is ahead of his wife? What is the best way to tackle such problems? ...
0
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1answer
18 views

Slack variable and counting integer solutions

So, I'm now familiar with the stars and bars method, but something struck my mind. To calculate non-negative integer solutions to $x_1+x_2+x_3+\cdots+x_n = k$ we use the Stars and Bars method. ...
1
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2answers
93 views

The probability that in a word made from a set of 16 letters exactly two are repeated

A word of 6 letters is formed from a set of 16 different letters of English alphabets (with replacement). Find the probability that exactly two letters are repeated. The answer is ...
3
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4answers
71 views

Number of ways to choose a pair $\{a,b\}$ of distinct numbers from the set $\{1,2,…,50\}$

Find the number of ways to choose a pair $\{a,b\}$ of distinct numbers from the set $\{1,2,...,50\}$ such that i) $|a-b| = 5$; ii) $|a-b| \leq 5 $ My thoughts: For (i) For every 6 consecutive ...
0
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1answer
145 views

Combination with selective boundaries

Im in a statistics course and I am honestly quite stuck on this problem. I really would love some guidance! "A shelf contains 9 different fiction books and 6 different nonfiction books. A woman ...