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Questions tagged [combinatorics]

Counting or enumerating elements in a set or other finite discrete structure.

2
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1answer
45 views

I need to know how many combinations are possible from these, if I must select at least one (but can choose more than one) from each table

I have a very simple permutation question that I can't figure out on my own. So, I have {A, B, C} and {D, E, F} I need to ...
1
vote
2answers
68 views

Formulaic way to calculate the numerator of a probability mass function?

Problem description A package contains six batteries. Two of them are defective. Suppose that we randomly select three batteries and test them for defects. What is the probability that ...
1
vote
1answer
48 views

About combinatorics

I have 5 Americans, 4 Mexicans, 3 Argentines and 2 Uruguayans. If I want to form a committee of 5 people, with the condition that each nationality is represented I know that I have to calculate the ...
4
votes
1answer
540 views

How many ways there are to add up 7 numbers to sum of 180?

Farmer has 7 pigs and 180 potatoes. How many combinations of distributing those 180 potatoes there are? Order does not matter. Each pig can get from zero to 180 potatoes, but all 7 pigs must get ...
5
votes
1answer
141 views

Finding optimal correspondences between objects given two square distance matrices

I would like to find the optimal correspondences between two systems of objects based on the distances between objects WITHIN the two systems. So, the input to the algorithm would be two square ...
2
votes
0answers
42 views

Rearrange 2D grid [closed]

I have a 2D grid on which I represent data points: Here, the red data point activates the grid on positions (1,1), (1,4) and (2,3). The blue data point activates the grid on positions (1,1), (4,3), (...
3
votes
1answer
83 views

Exactly 1 pair in 3 random cards from a poker deck

poker deck is 13 rank (2-Ace) and 4 suits for a total of 52 cards Draw 3 random cards what is the chance of exactly 1 pair (same rank)? using combination $$\frac { \binom{4}{2} \binom{13}{1} \...
0
votes
0answers
100 views

Why do we use combinations rather than permutations when calculating sample points

Let me state a question to use as an example: Suppose I have 3 blue marbles and 4 red marbles. Suppose we take 5 marbles from this without replacement. What would be the pdf of the random variable Y ...
3
votes
1answer
39 views

Committee forming: bad intuition, but where?

Consider the following problem: How many different mixed gender committees of 3 people can be chosen from a group of 5 men and 5 women? Wrong approach: These are committees of the form $...
2
votes
1answer
540 views

When to use ${13 \choose 1}\times{12\choose 2}$ and not ${13\choose 3}$

It's really a conceptual problem and I am looking for a good way to get the intuition right more often than chance. Typical occurence: count the number of poker hands containing exactly three cards ...
0
votes
0answers
21 views

Should I be using the Combination interpretation or the Permutation interpretation? [duplicate]

Question: A family has three children but you don’t know their sexes. If at least two are boys, what’s the probability one child is a girl (assuming that all outcomes are equally likely)? My Answers ...
1
vote
1answer
43 views

Given a set of bounded integers; find number combinations which sums to S [duplicate]

Consider that I am given a set of $n$ integers $a_1, a_2, \ldots a_n$, which can take any value in the interval $1\leq a_i\leq t$, where $t$ is a positive integer, how can I find the number of ...
1
vote
0answers
94 views

Combinations of Bernoulli Trials

I recently asked another question, which I have linked here: Combining Binomial Random Variables. I wanted to add onto that question, so I am asking in a different thread. Brief recap of previous ...
0
votes
1answer
405 views

Poker chance of straight or 8 outer straight draw on the flop from suited connectors 34 - TJ

Poker - 52 cards 4 suits of 13 (rank) cards each Poker probability Rank - ace (1) is both high and low so A23456789TJQKA Suited - Holding 2 cards of the same suit Connectors - 2 sequential (e....
1
vote
1answer
103 views

What is the probability of randomly picking 4 consecutive ladies out of a team of 11 people?

I was running the morning standup this morning and in contrary to the usual alphabetical order I announced I was going to go in "random" order today, however I then ended up giving all the ladies of ...
2
votes
1answer
41 views

probability that noone will have to wait for change [closed]

This is the exact question text: $2n$ children are waiting in a queue for movie ticket. Tickets are priced at a quarter each. Each child pays for the ticket either with a quarter or with half dollar ...
2
votes
2answers
80 views

Probability that 2 out of 3 friends win a raffle?

Let's say it's me and 2 other friends are at a raffle. There are 10 total participants. 3 of the 10 of us will win something, I don't care about what we win. A person can't win more than once. What is ...
2
votes
0answers
83 views

Poker make a flush with suited starting hand

Poker - 52 cards 4 suits of 13 (rank) cards each Poker probability A flush is 5 cards of the same suit The chance of a flush in 5 random cards is: $$\frac { \binom{13}{5} \binom{4}{1}} {\binom{...
3
votes
2answers
522 views

How many combinations of K ordered numbers from N numbers list

I have N numbers, 1-N (my N is 70). I need to know how many combinations of sequences of K numbers (K is 8 in my case) are possible, where the sequence is always increasing. Examples: 1,6,23,45,51,...
3
votes
4answers
167 views

10 cards out - chance of 2 aces out

Poker - 52 cards 4 suits of 13 cards each A deck will have 4 aces Let say 5 player - 10 cards pre flop Poker probability What is the chance exactly 2 aces are out (in the 10 cards dealt)? Is ...
4
votes
1answer
1k views

Ways to make a straight in poker

A deck is 4 suits of 13 cards each. The ace is both low and high so that is why you have 10 ways to make a straight. A flush is all cards of the same suite. There are two hands (flush and full house)...
1
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0answers
49 views

Looking for canonical problems or seminal work it the intersection of constraint programming and statistics

I'm interested in exploring the area (if it exists) at the intersection of constraint programming and statistics. My primary interest is on problems that require a combination of both statistical and ...
2
votes
0answers
83 views

Relationship between CLT for estimator of sample and number of combinations for subsample?

What is the relationship between the Central Limit Theorem as applied to the expected value of an estimator of a parent sample and the number of possible combinations of a subsample used to calculate ...
0
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0answers
93 views

Sampling combinations

I'm running a simulation where the different inputs are combinations of $n$ values taken in $r$. The problem is that even though $n$ is small, the number of different combinations is very large, so I ...
1
vote
0answers
56 views

Show that a random variable is distributed as a Geometric rv

I am working on an assignment: I have a line of numbers that is divided in intervals of fixed length, so for example: [0,c), [c,2c), [2c,3c), etc. Each interval is numbered 1,2,3 etc. X is an ...
1
vote
1answer
32 views

Unique vectors that can result from bootstrapping

My question concerns the unique number of vectors that can result from bootstrapping. Ie I have a vector of length 12 with the following elements : 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1 and I would like to ...
2
votes
1answer
2k views

Poker how many ways to make 4 of a kind

In this link it say there 13 X 48 = 624 ways to make 4 of a kind from card deck Where does the 48 come from? I can get 4! = 24 but I cannot get the 48
10
votes
2answers
337 views

What is the distribution of the cardinality of the intersection of independent random samples without replacement?

$S$ is some set with $n\in\mathbb{N}$ elements, and $a_1,a_2,...,a_m$ are fixed positive integers less than or equal to $n$. With the elements of $S$ being equally likely, $m$ samples $L_1, L_2,...,...
11
votes
2answers
1k views

Probability that Secret Santa arrangement will result in perfect pairings

So, we had Secret Santa at work. We're 8 people. We each took turns and pulled a small piece of paper from a bowl with a name on it. The only rule : If you pull your name, you have to put the piece ...
11
votes
2answers
218 views

The “strongest password”

I have an app which is protected by a four-digit-PIN and the user got five attempts at logging in before the account is locked. Now, one of my customers wants to "strengthen" the security and ...
2
votes
1answer
53 views

Probability distribution of randomly drawn summed ranks

I have a sequence of N unique values which are ranked 1 to N. A subset are those in positions 1 to n where n < N. An ideal system of ordering would put the lowest ranks 1 to n in the first n ...
0
votes
1answer
76 views

Probability about student test

i am reviewing about statistics and probability questions but i do not have answers for it and i am uncertain that my answer done well. Here is the question. In a test, student have to answer 8 out ...
1
vote
1answer
692 views

Generating random samples in N dimensions in Python [closed]

I am trying to generate N random samples in J dimensions subject to a constraint. Each dimension j is bounded by a unique "Lower_Bound" and "Upper_Bound," which both are bounded [0,1]. The ...
3
votes
1answer
189 views

Which is the maximum number of combinations between two populations

I have two populations of size N1 and N2: pop1 = {a,b,c,d,e,f,g} and pop2 = {h,i,j,k,l} I want to produce combinations of this two populations swapping individuals between the two but keeping the ...
0
votes
2answers
66 views

Basic question in combinatorics

I am studying basic statistics for fun. I have been reading about simple combinatorics as the first step. I am trying to solve the following problems 8 identical items are distributed for 4 people. ...
0
votes
0answers
388 views

Combinations of substring occurrence in string

Say I have a binary sequence of length N (e.g. HTHHTHTTTTTTH). How do I find the number of ways to get a NON-overlapping substring of length K (e.g. HHTH), where 1<=K<=N? It's possible you can ...
1
vote
0answers
83 views

Probability of someone getting a straight flush in a 5 player game

Say you are playing a version of poker where you get dealt $5$ cards from a regular $52$ card deck. Also let's assume we have $5$ players. Question: What is the probability that at least one of the ...
10
votes
3answers
746 views

What are the statistical methods I can use to find popular or common combinations of categorical variables?

I am doing a study on polydrug use. I have a data sets of 400 drug addicts, who each stated the drugs that they abuse. There are more than 10 drugs and hence there large possible combinations. I have ...
3
votes
1answer
90 views

Calculate the probability of observing n elements in m draws from an uneven frequency distribution, in order but consecutive or not

I want to calculate the probability to observe a certain sequence of n elements in order, but not necessarily consecutively, after drawing m times from an uneven frequency distribution. For example: ...
1
vote
0answers
73 views

Expectation for number of stops

I was looking through old exam questions and stumbled upon a question in Henk Tijim's Probability Exam Questions and Solutions that rocked me, so I began to think of further questions. Here is the ...
7
votes
4answers
768 views

Magic Urn Problem

ADDENDUM: First off, thank you all for your insightful answers to this weekend, fun problem, and especially Mark L Stone for his initial comment. I'm probably missing the point in some of the answers, ...
0
votes
1answer
27 views

Basic question about assigning items to groups

Suppose there are 9 items, which are assigned to three groups. The first group may contain 2 items, the second 3, and the last one 4. In how many different ways the items may be assigned to the groups?...
3
votes
1answer
598 views

Potential Meld Point Range in Pinochle

I would like to be able to figure out what the meld potential (upper/lower boundaries as well as probability for each score) is for a given hand, ideally the solution would calculated for each suit. ...
2
votes
3answers
87 views

Number of combinations from a set with certain rules

Suppose I would like to select $m$ integers from the set $S=\{1,2,...,n\}$ with the following rules: 1) $j$ out of $m$ are necessarily distinct. Denote this as $S_1$ 2) the rest $m-j$ are selected ...
1
vote
1answer
147 views

Deck of Cards - Combination Question

The question asks to randomly draw 13 cards from a standard deck (52 cards). What is the probability that there are 3 aces in those 13 cards you drew. Let $n(s)$ be the number of $13$ card ...
0
votes
1answer
91 views

Basic Permutation Question

I've started studying permutations and I'm confused as to how to properly solve a problem. For example, select 4 digits from the set $\{1,2,3,4,5,6,7\}$ without replacement. What is the probability ...
1
vote
0answers
67 views

Probability of 10 (somewhat) consecutive events

My question to you: can you please tell me if I am doing things correctly or I am off base? Thanks! Objective: to determine the probability of 10 independent people having a one base pair mutation (...
2
votes
0answers
511 views

BIBD or IBD or PBIBD

I use block design for discrete choice experiment. While Balanced incomplete block design(BIBD) is considered as gold standard for blocking in choice experiments. However this is not always possible ...
4
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0answers
136 views

Combinatorial Block Designs in Statistics

How are combinatorial designs such as BIBD and Steiner triple systems used in statistics in designs of experiments and hypothesis testing.
8
votes
2answers
619 views

Probability of letters occurring in order in a string

Suppose we have an alphabet containing $m+1$ symbols, $\{a, b, c, d, e,..., \$\}$, where $p = \Pr(a) = \Pr(b) =\cdots$, and $\Pr(\$) = 1 - (\Pr(a)+\Pr(b)+\cdots)=1-mp$. For a random string of length $...