Stack Exchange Network

Stack Exchange network consists of 174 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [combinations]

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.

2
votes
3answers
27 views

$(2n-1)(2n-3)..3.1 = \frac{(2n)!}{2^nn!}$

Here is a question from the book An Introduction to The Theory of Numbers by Ivan Niven. Suppose that $\mathbb{L}$ contains $2n$ elements, and that $\mathbb{L}$ is partitioned into $n$ disjoint ...
0
votes
3answers
30 views

Count of $N$ digit numbers with no repeating neighbors

How many $N$ digit numbers are there such that neighboring digits are distinct and first and last digits are distinct too. For $2$ digits there are $9\cdot 9$ obviously. For $3$ digits it's $9\cdot ...
2
votes
1answer
19 views

A Question About The Addition And Multiplication Principles In Permutations And Combinations

I am learning permutations and combinations in school, and there is something confusing me about the addition and multiplication principle. There is a specific situation where I'm not sure if I should ...
2
votes
3answers
61 views

if there are 4 different tables and 18 people, how many ways can the people be seated to have at least 4 in each table?

For example with 15 people at 3 different tables each seating 5 people, is the number of combinations of seating equal to: $$\binom{15}5\binom{10}5(4!)^3$$
4
votes
2answers
400 views

Calculate lottery's second prize using combination - lottery probability question.

Assume a lottery game of the following rules: Picking your numbers: Pick a total of 6 different numbers from the lot containing 42 numbers (1 to 42). Draw: Draw 7 balls, with no repetition(i.e: ...
0
votes
1answer
38 views

In how many ways can a group of $6$ students be formed from among $40$? [on hold]

I have a math statistics assignment and I was wondering if someone could help. The first questions states: There are 40 students in a conference. In how many ways can a group of 6 students be ...
4
votes
1answer
46 views

Combinatorial Analysis - Specific problem

I am having difficulty modeling a combinatorial analysis on a particular problem, I wanted to isolate some generic form to count how many valid arrangements exist in a given problem, can anyone help ...
1
vote
2answers
26 views

Probability of 3 aces from drawing 7 cards. 1.58 Intro to Probability, 2nd Ed.

This is Problem 1.58 from Tsitsiklis, Bertsekas, Introduction to Probability, 2nd edition. We draw the top 7 cards from a well-shuffled standard 52-card deck. Find the probability that: a) The 7 ...
0
votes
0answers
12 views

Combination of m elements from the first half of an ordered set

I have an ordered sequence with $n$ elements: $\{1,...,n\}$. I would like to obtain all the possible combinations of $m$ elements using just the first half of $n$ (so the numbers from $0$ to $n/2$). I ...
0
votes
1answer
43 views

100 Cars in a parking lot, k are lemons. We sample m. What's the probability of a lemon?

This is Problem 1.59 from Tsitsiklis, Bertsekas, Introduction to Probability, 2nd edition. A parking lot contains 100 cars, k of which happen to be lemons. We select m of these cars at random and ...
0
votes
1answer
33 views

Removal of K objects such that no two are adjacent

There are $2$ rows joined side-by-side with $n$ objects in each row. What is the number of ways to remove exactly $k$ objects such that no two vacant places, after removal, are adjacent to each other? ...
5
votes
4answers
998 views

How To Tell When Order Matters Or Not

I have encountered a problem involving combinatorics: My solution to it was $(4\cdot3\cdot2)+(5\cdot3\cdot4)+(6\cdot5\cdot4)$. The textbooks solution to it, however, was I would understand the ...
3
votes
1answer
22 views

Combinatorics question involving distributing DISTINCT candies to DISTINCT children

Suppose you want to distribute 15 DISTINCT candies to 5 DISTINCT children: A, B, C, D and E. a) In how many ways can this be done (no restrictions)? b) In how many ways can this be done if each kid ...
2
votes
3answers
31 views

Combinatorics question involving distributing 9 different candies to three different kids

Nine different chocolate bars are to be distributed to 3 different kids. a) In how many ways can this be done if there are no restrictions? b) In how many ways can this be done if the child A ...
1
vote
1answer
18 views

Combinatorics Question involving a person inviting a different subset of friends to dinner each night

Suppose that a person with 7 friends invites a different subset of three friends to dinner every night for 7 consecutive evenings. How many ways can this be done so that each friend is included at ...
3
votes
1answer
24 views

Combinatorics question involving distributing identical candies to different children

Suppose you want to distribute 15 identical candies to 5 different children. a) In how many ways can this be done if every kid receives at least one piece of candy? b) In how many ways can this be ...
0
votes
0answers
18 views

Combinations of pairing of list elements

This question might need a bit of editing. I am trying to solve the following problem. Their are even Number of students. Their is list of Marks for each one of them (and 2 or more students can have ...
0
votes
0answers
29 views

Generalizable combination of combinations ratio equation

I have been trying to solve the following problem for a few days and any help or direction towards combinatorics literature would be appreciated. Given a starting sequence of length n, an index ...
1
vote
2answers
22 views

Different way of solving this combinatorics question.

In an examination, a question paper consists of 12 questions divided into two parts i.e, Part I and Part II, containing 5 and 7 questions respectively. A student is required to attempt 8 question in ...
9
votes
4answers
827 views

What's wrong in my solution? Ways of choosing 5 items from 3 catagory with 3, 6, 14 items, while having 1 item from each catagory.

The exact question is: b) Sandra wishes to buy some applications (apps) for her smartphone but she only has enough money for 5 apps in total. There are 3 train apps, 6 social network apps and 14 ...
-1
votes
0answers
7 views

Selection and arrangements of distinct objects [on hold]

In how many ways can 7 people be seated around a circular table having 9 seats?
0
votes
1answer
25 views

8-element permutations of a multiset {3:0,1:1,1:3,1:5,1:8,1:9} with the restriction 0 is not allowed in left or rightmost position

I am lost in how to approach this problem due to the wording: Count the number of distinct 8-digit numbers that may be made by permuting the multi-set: $$MS:=\{0:3,1:1,3:1,5:1,8:1,9:1\}$$ ...
0
votes
2answers
35 views

how to make pairs from odd number of people one may be alone?

How Many ways the pairs can be formed from the group of size odd(like 3,5), one may be left alone? Eg: there are 5 students, so 2 pairs can be formed and one guy left alone... |Consider (a,b,c,d,e) ...
2
votes
2answers
34 views

Figuring out how many ways 5 marbles can be drawn (combination/permutation problem)

A bag contains 24 marbles, 4 red, 12 green, and 8 brown. How many ways can 5 marbles be drawn with all 5 marbles green. I know you can consider that there are just 12 green marbles and 12 not green ...
2
votes
1answer
39 views

Combinatorics question involving assigning students from high schools to colleges

There are 15 different students, 3 students each from 5 different high schools. There are 5 admission officers, one from each of 5 colleges. Each of the officers successively picks 3 of the students ...
0
votes
0answers
17 views

What do we call this pairing problem that is subject to this constraint?

Suppose there is a set of randomly generated floating point numbers $z = \{z_1, z_2 \dots z_N\} = 1 $ and two sets of discrete positive numbers $x = \{x_1, x_2 \dots x_N\}$ and $y= \{y_1, y_2 \dots ...
0
votes
1answer
51 views

$n$ balls that are colorless. You choose $k$ balls, paint $b$ of these balls blue, and paint $r$ of these balls red?

Suppose you have $n$ balls that are colorless. In how many ways can you choose $k$ balls, paint $b$ of these balls blue, and paint $r$ of these balls red? I have to count this in $2$ ways, right now ...
3
votes
2answers
37 views

Combinatorics Problem involving separating different colored balls

You want to arrange $5$ identical white balls, $4$ identical red balls and $3$ identical blue balls in a row. a) In how many different ways can this be done? b) What if we are required that all ...
1
vote
0answers
25 views

Calculate probability of drawing at least 3 objects given certain conditions (in body paragraph)

Just need some help solving this question, the "at least 3" instead of "exactly 3" makes this difficult, I'm not sure where to start. Assume there are 8 bags in front of you, all containing marbles ...
0
votes
0answers
17 views

Total Possible Combinations when exhausting a group [on hold]

I have 3 green basketballs, 2 red, 6 yellow and 4 green. How many combinations are possible if I shoot one basketball at a time with the stipulation that once a color is chosen, I have to shoot all of ...
0
votes
0answers
28 views

Combinations of $64\times64$ image

I have a $64\times64$ image where the pixels can have either $0$ or $1$ value. I want to divide $0$ and $1$ equally between all the pixels. Nowhere are two cases: 1) where the order of pixels don't ...
1
vote
1answer
39 views

How many ways are there to pick a lock?

A passenger left his belongings inside a locker at an airport. When he wanted to get his belongings, it turned out that he forgot the number. He only remembers that it has numbers $23$ and $37$ in it. ...
-2
votes
0answers
37 views

Number of ways to seat people in a rectangular seat arrangment [on hold]

Their is an (2 X n) size seat arrangement is given and we've to make m people sit in this seat arrangement , such that no two people share a side . example n=3 m=2 their are 8 ways of seat ...
1
vote
2answers
31 views

In how many ways can I put 1 to 5 mirrors in 8 rooms?

A queen has 8 rooms and 12 indistinguishable mirrors, how many ways are there to hang these mirrors in 8 rooms such that every room has at least 1 mirror?
1
vote
1answer
24 views

Combinations of 7 people out of 30

A small kingdom wants to choose their king, his advisor and 5 guards, how many ways are there to choose them? $30 \choose 7$? Why? Why not?
0
votes
1answer
30 views

How to create subsequences from a set of ordered integers given the specified constraints.

Given, for example, the following set of integers $\{1,2,3,4\}$, how can you compute the number of all possible sequence scenarios, where a scenario consists of a number of sequences, as following ...
-1
votes
1answer
20 views

Calculate the number of ways to mix up colored cubes

Imagine you have three blue, and three red cubes. The question now would be, how many ways are there to arrange these six cubes? One colour sequence is one way to arrange them. The solution for three ...
0
votes
0answers
29 views

The probability of drawing all black balls in all balls without replacement.

There are two kinds balls, one is a black ball and the other is a white ball. If there is only one black ball and one white ball, the probability of drawing a black ball is $p$. Now, we assume that ...
1
vote
1answer
44 views

Expected number of random choices required to find all combinations [closed]

If I have $n$ urns each containing $m$ distinct items, where the the urns are disjoint sets, and I repeatedly draw an item from each urn with replacement to make an $n$-combination, how many such $n$-...
1
vote
1answer
27 views

How many unique games can be created from a deck of 25 cards?

I'd love some Math help. This Math question is probably too complicated to be solved. I've created a board game that has one important part that uses cards. I'm having trouble coming up with the ...
3
votes
2answers
19 views

Combinatorics Question on distribution of identical and distinct gifts.

How many ways are there to distribute $3$ different teddy bears and $9$ identical lollipops to four children: (a) without restriction? (b) with no child getting greater than or equal to $2$ teddy ...
0
votes
1answer
20 views

Binomial Distribution Question, Cannot figure out process

I am really stuck on this question on my last homework and did not have time to stop by office hours. If anyone can walk me through this, I would really appreciate it. A marksman scores a bull's ...
4
votes
1answer
30 views

Combinatorics question on number of integer solutions given different restrictions

How many nonnegative integer solutions are there to $$x_1 + x_2 + \ldots + x_5 = 20$$ (a) With $x_i \leq 10$? (b) With $x_i \leq 8$? (c) With $x_1 = 2x_2$? Here is what I did: (a) ${24\...
0
votes
1answer
32 views

$10$ questions selected from a bank of $25$ questions. Easiest question first and hardest question always last. # of different ways.

$10$ questions selected from a bank of $25$ questions. Easiest question first and hardest question always last. # of different ways? I calculated the number of ways with no conditions was $...
0
votes
0answers
21 views

Arranging 3 types of balls

Say we have $3n$ balls of 3 types: 1,...,n big balls 1,...,n medium sized balls 1,...,n small balls I'd like to arrange them in triples so that every triple contains one of each type, but in each ...
2
votes
2answers
42 views

Given 24 computers and 6 broken computers, how many of the following different combinations are there?

As per the title: Consider 30 distinct computers. 6 of these computers are broken. How many ways are there of choosing 4 of any computer 4 computers with exactly 2 broken computers 4 computers with ...
0
votes
1answer
124 views

Another interesting seating problem [duplicate]

We all know about the standard seating with restriction problem in Combinatorics. We are given $n$ seats and $k$ people and we need to find a seating arrangement in which no two people sit together. ...
0
votes
0answers
21 views

Number of ordered triplets $(x, y, z)$ if $x, y, z \in \{1, 2, 3, 4, \ldots, n\}$ such that $x \geq y$ and $z \geq y$

I'm a little confused about this question as my answer is different from the book I'm solving. Question :- Find number of ordered triplets $(x, y, z)$ if $x, y, z$ belong to $\{1,2,3,4, \ldots, n\}$...
0
votes
0answers
19 views

How can I figure out the number of ways that more men than women are selected?

Twelve men and ten women apply to attend a special event. Six names are selected. In how many ways could more men than women be selected?
2
votes
1answer
34 views

5 digit numbers in ascending order

How many $5$ digit numbers are there such that digits are in ascending order ? I think it must be $5 \times 6^4$ , But I'm not sure. I would love to see an algorithm to solve this kind of problems.