Tagged Questions

5
votes
4answers
71 views

$n$ balls into $n+1$ urns (with one special urn)

Assume that there are $n$ balls numbered from $1,2,\ldots,n$ and $n+1$ urns, numbered as $0,1,\ldots,n$ Throw each ball randomly into one of $n$ urns: urn 1, ...
1
vote
2answers
136 views

Probability of having $k$ empty urns after putting $n$ balls into $n$ urns

Assume that there are $n$ balls (numbered from $1$ to $n$) and $n$ urns (numbered from $1$ to $n$). At the beginning no ball is placed in any urn. Balls are randomly thrown into urns: Each ball is ...
1
vote
3answers
58 views

n+1 balls put into n bins. Double count?

Question: n+1 balls are put into n bins. What is the probability that all of the bins are not empty (contain 1 ball at least)? What I did: Choose n balls from the n+1 ${n+1 \choose n}$, order them ...
0
votes
0answers
109 views

Balls and Bins problem with constraint

Assume we have $B$ black balls and $R$ red balls, where $R+B$ is a multiple of 4. We want to distribute the balls in $\frac{R+B}{4}$ bins such that each bin has at least 1 red ball and at least 1 ...
1
vote
2answers
67 views

Probability of red ball i before any black ball

Assume we have $r$ red balls and $b$ black balls in a box and we remove one ball at a time without replacement. Red balls are labeled from $1$ to $r$. We want to calculate the probability a particular ...
1
vote
1answer
96 views

Arrangements with No Two Vowels Consecutive

In general we state that there are ${r-wn - (n-1) \choose (n-1)}$ ways to distribute r identical balls in n distinct boxes with at least w balls in each box. Considering this, how many ways are there ...
0
votes
1answer
109 views

Bins in balls where bin size grows exponentially

I have $k$ bins. The first bin can fit $1$ ball. Each subsequent bin can fit two times more balls than the previous one. In other words, the $i$th bin can fit $2^i$ balls. We randomly assign $U = ...
0
votes
0answers
50 views

Simulating the balls and bins problem in Mathematica (or similar)?

The 'balls and bins' problem Distribute $n$ balls into $d$ bins in a way which minimises the difference between the highest and lowest loaded bins. Reasoning for performing simulation I have some ...
7
votes
5answers
193 views

Probability that all bins contain strictly more than one ball?

Here's the problem I'm working on: Given that I'm distributing $N$ balls into $K$ bins, what is the probability that all bins contain at least two (strictly more than 1) balls? This seems like a very ...
2
votes
1answer
266 views

In how many ways can 2 balls be arranged in 5 boxes so that one box does not contain more than one ball?

What is the number of ways 2 balls can be arranged in 5 boxes? The boxes may not contain more than 1 ball. The balls are of different colors. I forgot to mention the order of the boxes are important. ...
0
votes
0answers
56 views

What is the chance that a box is empty after randomly filling it with balls? [duplicate]

Possible Duplicate: If n balls are thrown into k bins, what is the probability that every bin gets at least one ball? Suppose that I randomly distribute $n$ balls into $m$ boxes. What is ...
9
votes
1answer
214 views

Hyper Birthday Paradox?

There are $N$ buckets. Each second we add one new ball to a random bucket - so at $t=k$, there are a total of $k$ balls collectively in the buckets. At $t=1$, we expect that at least one bucket ...