# Questions tagged [combinatorics]

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

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105 views

### Poker Calculator

Wrote a program to rate 2 hole cards (your hand) against a single random hand. Your two hole card are combined with a common 5 card board to create the best 5 card hand. You can play the board. ...
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### Probability of observing all cards? [duplicate]

I have a stack of $n$ distinct cards. I randomly draw $N$ cards from the stack with replacement. Assume that $N \ge n$. What is the probability that I observe all cards at least once? I got this far:...
54 views

Let's say we had the word STATISTICS, and it was hanging on a wall, then two letters in the word blew off, and somebody found them. What are the chances they put them in the correct order? here is ...
42 views

### Counting outcomes from arrangements of 4 bags

I'm having issues solving an introdutory exercise in a probability course. The following problem description is similar but not equal to the one I'm solving. I will first state the problem, then I ...
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### Sampling pairs without replacement from two urns with overlapping populations

I have been trying to derive the coefficient of inbreeding lately, but I am at a loss. If I understand correctly it measures the probability of an allele "collision" i.e. getting the same allele from ...
106 views

### how do you calculate the number of combinations recursive partitioning uses in decision trees?

So I was wondering why random forests limit the levels of a variable to 32 levels, and I found an answer here : R's randomForest can not handle more than 32 levels. What is workaround? My ...
122 views

### Permutations in an Urn Problem, with Finite Number of Balls

In general I think I understand permutations fairly well. A simple example of permutations is drawing balls from an urn. I have 3 colors of balls, blue, green, and red, and I have 5 balls of each....
75 views

### Combination multiplication and joint probability of independent events probability

Is there direct correspondence between the rule of multiplication of combinations and probability multiplication in case of independent events? For combinations, whichever cup I choose, I can chose ...
85 views

### number of different events in a random sequence

I'm confronted with a probability problem that may have already been solved. I'm considering random sequences of m events. The number of possible events is n, and each type of event has the same ...
42 views

### Help with this combinatorial computation

I am going to run a test with N subjects. There are M=50 stimuli to be evaluated by the subjects but, for time and concentration reasons, a subject cannot evaluate all the stimuli. Therefore, I am ...
606 views

### Expected value of the largest number drawn in n drawings

An urn contains balls numbered 1 to N. Let X be the largest number drawn in n drawings when random sampling with replacement is used. (The event X k means that each of n numbers drawn is less than or ...
32 views

### probability of a digit repeating anywhere within a string [duplicate]

This is purely for interest. So I received from my bank a randomly generated (?) login code which is a string of 9 numerical digits (0-9). 5 of these 9 digits were the same number (but not in ...
104 views

### Probability of choosing all the numbers in a set

Suppose you have $m=5$ people and $n=4$ numbers. Each person chooses, independently and at random, one of these numbers. What's the probability that all the numbers will be chosen? I've been able to ...
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### Looking for interdisciplinary research topic [closed]

TL;DR: Are there any areas that combine (1) statistics/ML, (2) computation theory, (3) set/type theory, and (4) real/functional analysis? I apologize if I did not accurately categorize the domains ...
135 views

### How to calculate the number of all combinations of all permutations?

I have a set n with m elements. I aim for the number of all combinations of all permutations of all elements of the set. An minimal example would be with a two element set [1,2]: All permutations of ...
74 views

### Fairness of a Coin. Number of heads vs probability of permutation

If I look at a sequence of 100 coin tosses and I get 90 heads the probability of the coin being fair vs not fair is a lot lower as answered in a lot of questions already. But when I go from looking at ...
1k views

### You randomly select two distinct integers between 1 and 100. What is the probability that the larger number is exactly twice the smaller number?

I recently took a HackerRank test for a Data Science position and got this question wrong. I came to 1/200. Here's how: There are 50 combinations that will make ...
114 views

### Calculating the expected time

Assume we are trying to crack a password. There are $2^{88}$ possibilities. I have a machine that can test $2^{40}$ passwords per second. What is the expected time to find the password if I use ...
439 views

### How to calculate the probability of an event occuring within n days, if we know the probability of it occuring per day

If an event can occur at most once per day, and the probability of it occurring is 10%. What is the upper-bound on the probability that the event occurs in an interval of L days of a month (assuming ...
2k views

### Dividing data into two groups as similar as possible

In this simplified example, I have five variables for each individual. The data is normalized, with mean 0 and sd 1 in each variable. I would like to divide this data into two groups with equal size ...
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### confused with group testing

These are from notes,and I'm just very confused about what it tries to say Question 1: Does each test test all items? For example, if test 1 tested all items, test 2 tested all items etc, then why ...
141 views

### How to efficiently sample a large number of unique binary vectors

This is probably just a basic CS question, so I appreciate the help. I'm doing Monte Carlo permutation tests in matlab for One-Sample and Paired Two-Sample Tests (where there are x^n unique vectors ...
65 views

### Combination versus fraction

This happens to be about poker but I would like to ask it in a general way There are 47 cards remaining in the deck with 2 cards to come Of the 47 cards 9 make my hand - I only need 1 but 2 two ...
1k views

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### Counting the number of combinations from 5 equals sets

I have 5 sets with three elements each: A can be either 2,1 or 0 B can be either 2,1 or 0 . . E can be either 2,1 or 0 You can only pick one element from one of ...
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### Need help calculating number of possible passwords with given criteria

I need help calculating the number of possible passwords with a given set of criteria. Here is the set of criteria: Passwords are case insensitive. Must be 6-14 characters. Must contain at least 1 ...
185 views

### Card deck shuffling, what is the probability that four lowest card of a suit are distributed to all four players?

In 4-player trick-taking game where taking a trick constitute a penalty (e.g. Hearts), I've often seen the card 5 (the fourth-lowest rank in a suit, when 2 is the lowest and Ace is the highest) takes ...
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### 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 ...