# Questions tagged [balls-in-bins]

For problems on the distribution of $m$ distinct or identical balls into $n$ distinct or identical bins, optionally with restrictions.

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### What is the probability of getting a red ball exactly $n-2$ times? [closed]

Problem An urn contains $3$ white balls and $5$ red balls. $n$ balls are drawn successively in such a way that at each drawing they’re still within the realm of possibilities, so $3^n$ drawings total. ...
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### Ballot problem with tie

We have two candidates $c_1$ and $c_2$. At the end of a ballot each candidate receives $p$-many votes. What is the probability that $c_2$ has never been ahead of $c_1$ the whole process of vote ...
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### ball and bins probability

If there are k bins and n balls are randomly thrown into the k bins (equal chance of every ball going into any bin) and then we randomly select a bin, what are the odds that the randomly selected bin ...
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### Probability that fourth number is greater than first number

We have a bag which contains $49$ numbers. We draw $6$ numbers randomly without replacement. What is the probability that the fourth number is greater that the first one? My approach: First we define ...
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1 vote
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### How many ways are there to put seven white and two black billiard balls in nine pockets? Some of the pockets may remain empty and the pockets are cons

How many ways are there to put seven white and two black billiard balls in nine pockets? Some of the pockets may remain empty and the pockets are considered indistinguishable. Well, my solution goes ...
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1 vote
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### Distribution of $10$ different marbles to $6$ different color boxes

The question is: There are $6$ boxes, with each box a different color, and $10$ different marbles. The marbles are scattered randomly in the boxes. What is the probability that all marbles are in ...
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### Classic Picking Balls from 2 Urns Question

The question involves 2 urns, URN1 and URN2. There are 18 balls of 4 variations in URN1: 3 Red Balls, 5 Orange Balls, 5 Yellow Balls and 5 Green Balls. There is 1 ball of unknown color in URN2, i.e. ...
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### Distinct Objects into Distinct Bins, each bin has a different number of objects

I was curious about these types of distribution and combinatorics problems and going about solving them. Let's say there are 15 different fruits that are to be equally likely distributed among 6 ...
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### Given N balls and M buckets(N > M), what is the probability that every bucket has at least one ball in it? [duplicate]

In reality, I want to find the probability that at least one bucket is empty. But I'm not sure whether it is easier to calculate that or do 1 - P(every bucket has a ball in it).
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### n black balls k white balls in M bins, what is the probability of selecting a black ball from any bin.

There are $n$ black balls and $k$ white, with $M$ bins. The process for filling the bins is as follows: Consider each of the $N=n+k$ balls, one at a time. For each ball, select 1 of the $M$ bins ...
1 vote
58 views

### Confusing in the solution of indistinguishable balls in distinct urns

This question was taken from Mathematical Statistics and Application $7$th edition page $85$ , question $2.181$ Suppose that n indistinguishable balls are to be arranged in N distinguishable boxes so ...
1 vote
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### Balls in urns with different max capacity for each urn

I'm looking to figure out the formula for putting K balls in N urns, where each of the N urns has a specific max capacity. For example, Urn A has capacity for at most 5 balls Urn B has capacity for ...
1 vote