# Questions tagged [combinatorics]

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

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### Making 3 comparisons with a ternary variable

I have a study in which I want to study the effect of a ternary variable $x$ in interaction with a binary variable $y$. The ternary variable is categorical, and for some reasons, I want to do the $3$ ...
1 vote
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### 10 identical socks, 7 drawers: What is the probability that at least one drawer contains 3 or more socks?

My nephew asked me the question thinking I would answer him very quickly, but I got stuck until today..... There are 7 drawers and 10 socks, all the same. The socks are randomly distributed in the ...
25 views

### Combinatorics question

Let me preface this by saying that this might be a trivial question for some of you. I want to find a formula that will help me automatically calculate the number of occurrences of certain kind of ...
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### Optimizing Treatment Group Assignments

When setting out experiments, I want to make sure treatment groups are as balanced as possible. Instead of using randomization, I've started to use the following process. I first collect some ...
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### Stochasticity challenge

If a string of characters (S) that is 325384 long, contains 458 As and 22 Bs. What is the probability that if the 458 As and 22 Bs were randomly positioned along the 325384 string of characters that ...
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1 vote
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### Probability of seeing an ace before seeing a two in a 52 card deck?

We have a shuffled, standard 52 card deck with 4 Aces and 4 twos. I am confused about the probability of seeing an ace before seeing a two. By symmetry, it seems obvious that the probability should be ...
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335 views

### Flipping an unfair coin until there are more heads

I came across this question on Quora. You have an unfair coin for which heads turns up with probability $p=\frac 35$. You flip the coin repeatedly until there have been more heads than tails. How ...
38 views

### Probability of not detecting fire if two of the sensors don't work well

I am trying to solve the following problem of probability: "In a certain factory, there is an alarm system composed of 5 sensors that work independently to detect fire. The probability that a ...
• 111
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### Number of ways you sit next to your friend with 4 other people at a round table [closed]

This is a question I have after seeing Q1 of this question. There are a total of 6 people including you and your friend, and you guys are about to sit at a round table. The method of counting the ...
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### $n$ people each randomly assigned a number from $1$ to $m$ with replacement. Probability that exactly one number is assigned to more than one person?

Suppose that $n$ people are each randomly assigned a number from $1$ to $m$ with replacement. What is the probability that exactly one number is assigned to more than one person? What I have tried: ...
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141 views

### Deterministic formula for average number of unique items picked

I am curious how to formulate a deterministic answer to a problem I have in mind. I have computed it stochastically, but am unsure of how to frame and compute the problem deterministically. My prob &...
1 vote
28 views

### Given a set of random variables, how can I find a linear combination of these variables satisfying a constraint on the sum of their permuations?

Say I have n random variables, {X0...Xn}, n>9. I also have another set of random variables constructed from the first set, where each of these are the sum of 9 ...
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