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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No: of ways to distribute cards .

In how many ways can a person send invitation cards to $6$ of his friends if he has $4$ servants to distribute the cards ? $a.)\ 6^{4}\\ \color{green}{b.)\ 4^{6}}\\ c.)\ 24\\ d.)\ 120$ As the ...
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0answers
20 views

Discrete mathematics combinations with repetition?? [on hold]

A bagel shop has onion bagels, poppy seed bagels, egg bagels, salty bagels, pumpernickel bagels, sesame seed bagels, raisin bagels, and plain bagels. How many ways are there to choose a) six bagels? ...
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2answers
29 views

Grouping 15 rating grades in 10 buckets

I am trying to group 15 corporate rating grades into 10 buckets. The grouping cannot be done in a random way - for example the rating grades 1 and 14 cannot be in a single bucket (constraint). The ...
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1answer
14 views

Name generator prefix+suffix

By googling "word permutation" and "word combinations" I found http://textmechanic.com/Permutation-Generator.html But I would like to send a bulk of prefix and suffix into an engine, and let it give ...
2
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0answers
26 views

About the least common multiple of numbers and combinatorial

Prove that for any positive integer $n$, the least common multiple of the numbers $1, 2, 3, \ldots , n$ and the least common multiple of the numbers: ${n\choose 1}, {n\choose 2}, \ldots , {n\choose ...
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1answer
25 views
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1answer
28 views

All Possible Pairs of 18 [duplicate]

I will be having 18 Students in my class this year. I'd like to have them learn in pairs rotating every day with a different student in the class. What are all the possible pairings. for example on ...
3
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1answer
34 views

Αn exercise in combinations.

Let it be $m,n\in\mathbb{N}^\ast$.Find the displaying numbers of $f$:$[m]$ $\rightarrow$ $[n]$ when: i)There are no restrictions ii)Is $1-1$ iii)Is strictly increasing iv)Ιs increasing My ...
0
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1answer
23 views

Different sums by adding the currency.

How many different sums can be formed by the following $5$ dollar, $1$ dollar, $50$ cents, $25$ cents, $10$ cents, $3$ cents, $2$ cents, $1$ cent. As there are $8$ different things and at ...
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1answer
21 views

combinatorial: 8 menbers of a team in four rooms.

Eight members of a basketball team should stay in a hotel. The hotel has a triple, two doubles and a single. How many ways can be distributed in different rooms ?. I have in mind the rooms of two ...
2
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3answers
29 views

The number of times will an individual child goes to the cinema before a group is repeated.

$1.)$ A mother with $7$ children takes $3$ at a time to a cinema.She goes with every group of $3$ that she can form.How many times can she go to cinema with distinct groups of $3$ children? ...
0
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0answers
27 views

Calculating Combinations / Permutations [closed]

How do I calculate the number of outcomes as a whole of a series of individual tests with there own outcomes? For example, the best description I could think of would be: There are 10 tests and each ...
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0answers
21 views

Distributions of identical and distinct objects [closed]

I'm having an issue figuring this problem out. I'm not sure how I should go about it exactly, all I know is that it needs to divided into stages, each its with its own set of cases. So here's is ...
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0answers
39 views

Non repeatable combinations [closed]

There are 10 girls and 15 boys in class. They're preparing zumba dance for the final show. The teacher decided that boys are doing better and only boys will play 3 zumba dances. Every each of them ...
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2answers
30 views

Further Improvised Question: Combination of selection of pens

Following from my first improvised question here and the two excellent answers given, here's another twist to the question. What happens if the total number of pens to be selected is $15$ instead of ...
-4
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0answers
21 views

groups of colors in a colorful cube - combinatorics [closed]

find natural number n, such that in every paint of a cube $$ 2^{[n]} $$ with the seven colors of the rainbow : a) there is 3 different groups $$ A, B , A \cap B $$ with the same color b) there is 3 ...
0
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2answers
37 views

Combination lock with continuous attempts

The lock has 4 symbols (A,B,C,D) and the password is 3 symbols long. Now, the lock does not "rest" after each attempt. So if I enter "ABCD" and the password is "ABC" or "BCD", it would open. I tried ...
2
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2answers
153 views

Improvised Question: Combination of selection of pens

This is a improvised version of the question here. Supposing there are four brands of pens, W, X, Y, Z. You want to choose $10$ pens made up of any combination of the brands, but limited to a ...
0
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1answer
50 views

How many different words can be formed using the letters of the word “ PERMUTACION”?

Is there any guide to solve this? Edit: This is what I do. I used the permutations. Please check if I did the right thing? Since 11 words so i did 11Pr 1 letter 11p1 2 letter 11p2 11 3 letter ...
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0answers
21 views

In a special deck of playing card, one which doesnt contain any Jack, Queen or King [closed]

Determine the probability of the following events: a. Drawing a space (one card) b. Drawing a black card (one card) c. Drawing of four hearts ( four card) d. Drawing of full house (five cards) e. ...
5
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4answers
147 views

Combinatorial Proof for Binomial Identity: $\sum_{k = 0}^n \binom{k}{p} = \binom{n+1}{p+1}$ [duplicate]

I am studying combinatorics and I came across the identity $$\sum\limits_{k=0}^n \binom kp =\binom {n+1}{p+1}.$$ I have read the algebraic proof and it does not appeal to me. Is there an elegant ...
0
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1answer
55 views

Probability that the tenth card is black if at most one was black out of the first nine

Assume you draw 10 cards from a standard 52 card deck without replacement. What is is the probability the 10th card is black for the two cases below: a) the first nine cards drawn are not ...
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3answers
63 views

How many ways can 6 cars ( 3 pink, 2 orange and 1 yellow) be parked in 6 parking slots in a row?

a. If the pink cars must be park together? - my answer is 4!3! or 144 b. If the orange cars must not be parked together? c. If you can't park the yellow on either end? d. If a pink car must be on ...
0
votes
1answer
18 views

Formula for finding the number of lists that can be created by selecting elements of other lists

I have List1 = {A,B} List2 = {C,D} List3 = {E,F} List4 = {G,H} A program will print a final list composed by only one letter from each list. So one of the ...
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1answer
40 views

How do I find the number of solutions of the equation $r_1 + r_2 + … + r_k = n$

I was studying the multinomial theorem: $(u_1+u_1+...u_k)^n=\sum\limits_{r_1+r_2+...r_k=n}\dfrac{n!}{r_1!r_2!...r_k!}u_1^{r_1}u_2^{r_2}...u_k^{r_k}$ and my book said that the number of terms in the ...
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1answer
39 views

Combinations of combinations problem

everyone. I'm faced with a problem that I cannot solve without error. There are 4 blanks. Each one of those blanks has a possibility of different letters/numbers. Here's the full problem. Blank one: ...
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votes
2answers
51 views

Combinations for the selection of 10 pens

I have a problem I'm not so sure how to solve. Here's what it says: A man needs to buy 10 pens at a store, there are 4 different brands W,X,Y and Z of blue pens, the pens that belong to each brand ...
0
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2answers
52 views

drawing red and black marbles

You have $4$ black and $2$ red marbles in a box. You draw $3$ marbles one at a time without replacement. The first two marbles you draw can either be (1) one black and one red, or (2) no black and ...
0
votes
1answer
58 views

How many 3-digit positive integers can be formed using the digit 0,1,2,3,4 and 5?

No repetition of digits? With repetition? If the integer must be greater than 400? (no repetition) If the integer must be even? If the integer must be odd? If the integer must be divisible by 5? (no ...
0
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1answer
39 views

Proof for the coefficient of $x^n$ in $(x^0 + x^1 + \dots + x^n)^n$

Theorem: The coefficient of $x^n$ in $(x^0 + x^1 + \dots + x^n)^n$ is $\binom{2n-1}{n-1}$. How to prove this? Multinomial theorem produces the following $$ \left(\sum_{k=0}^{n} x^k \right)^n = ...
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2answers
81 views

Find the number of natural number solutions of $a+2b+c=100$

Find the number of natural number solutions of $a+2b+c=100$ I remember something like stars and bars if the equation I change to $a+b_{1}+b_{2}+c=100$ then i get $\dbinom{99}{3}$ ways. If the ...
0
votes
1answer
22 views

How many ways can Nicole form a committee?

Nicole needs to form a committee of 3 from a group of 8 research attorneys to study possible changes to the Superior Court. If two of the attorneys are too inexperienced to serve together on ...
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0answers
29 views

What is the terminology of the collection of all possible combinations of the element of a set?

Let me explain my question better: Suppose I have a set $(1,2,3)$. Clearly, I have 6 ways to choose some elements from it: $$ (1),(2),(3),(1,2),(1,3),(2,3) $$ and I can make a collection to ...
3
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3answers
54 views

Grouping kids in Groups of $4$

How many different groups of $4$ can I create using $24$ students? I want to break my class of $24$ students into groups of $4$. I would like to create different groups each day until each student ...
1
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2answers
57 views

Combination of $n$ objects taken $p$ at a time where $n$ contains $r$, $s$, and $t$ identical objects.

I am talking about something like this: $ N = \{2, 3, 3, 3, 5, 5, 7\}$ $ n = 7$ $ s=3 $ $t=2$ In my case specifically, those numbers in $N$ are the prime factors of a number $Z$ repeated the number ...
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2answers
33 views

Combinations with repetition with limits.

From a Standard 52 card deck of playing cards. If 10 hands are dealt consisting of 2 cards each what is the probability of 3 of the hands being pairs? 4? 5? .... Is there a formula for this?
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2answers
76 views

In how many ways can 4 red, 3 blue and 2 green balls be arranged? [closed]

In how many unique ways can 4 red, 3 blue and 2 green balls be arranged if they are indistinguishable aside from color?
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0answers
22 views

possible number of arrangements for a group of 6 words

How many ways (possible combinations without repetition) can we arrange these words? ServiceInfo, TokenInfo, AccountInfo, DeviceInfo, LocationCoarseInfo, LocationPreciseInfo
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0answers
34 views

How to count the number of unique combination of numbers in a set N, whose products equal to K?

Let K be the number 32, and N be the set of its factors. K = 32 N = {2, 4, 8, 16} How many unique combination of numbers are there in N, whose product is equal to K ? The answer is 6, ...
2
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1answer
26 views

Selecting n balls from N - Cumulative Distribution Function

I am having difficulty with the following question: Suppose that N balls labelled $\{1, 2, . . . , N\}$ are placed in a box, and n balls ($n ≤ N$ ) are randomly selected without replacement. Define ...
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1answer
30 views

Probability of Group Standings vs. Randomized Standings

This question concerns MLB baseball standings. There are 6 divisions with 5 teams each for 30 total teams. Currently one division has three of the four best records. What are the odds that this ...
0
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2answers
45 views

Number of $k$ subsets of $S$ by choosing $i$ elements from $A$ and $j$ elements from $B$ where $S=A \cup B$

Let $A$ be a set with $m$ elements and let $B$ be a set with $n$ elements. Let $S=A \cup B$. Then the number of $k$-subsets of $S$ is clearly $C((m+n),k)$. However, if we want the number of $k$ ...
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2answers
38 views

Combinations of unknown number $n$

All members of a group play basketball, while all except one play ice hockey. The number of possible basketball teams of $5$ members each is the same as the number of possible ice hockey teams of ...
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4answers
74 views

Probability of visiting $4$ cities

On her vacations Veena visits four cities $(A, B, C\ \text{and}\ D)$ in a random order. What is the probability that she visits (i) $A$ before $B$? (ii) $A$ before $B$ and $B$ ...
0
votes
2answers
39 views

Find the total number of selections of r things from n different things when each thing can be repeated unlimited number of times?

Find the total number of selections of r things from n different things when each thing can be repeated unlimited number of times ? I know that the formula is $$ n+r-1\choose r $$ But how do we get ...
3
votes
3answers
48 views

Number of Non - Decreasing functions?

Let A={1,2,3.....10} & B={1,2,3....20}. We have to find the number of non decreasing functions from A-->B. What I tried :No. Of non decreasing functions = (Total functions) - (Number of ...
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3answers
883 views

With a standard deck of 52 cards, how many different 25 card spreads are available?

With a 52 card standard deck, if you need to deal 25 cards, how many different spreads are possible? For example, with a 2 card spread: ...
3
votes
2answers
43 views

Correctly calculating permutations and combinations without duplicate patterns

Given 16 balls each numbered 1 through 16, and 5 glass tubes numbered 1 through 5; how many ways are there to slot all 16 balls into the glass tubes, selected one at a time, with the only condition ...
0
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2answers
21 views

What are all the combinations in this case

I have 2 ordered sets: $\{A, B, C, D, E, F, G, H\}$ and $\{a, b, c, d, e, f, g, h\}$ I need to find all the ordered sets containing all $16$ of these elements, such that, The relative order of the ...
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0answers
26 views

Combinations within a Combination

Someone did it for me $20$ Years ago. It was using $12$ Numbers in this example $1$ to $12$ and there were $42$ sets of $6$ numbers. In that sample each of the $12$ numbers ONLY appears $21$ times, ...