It's about distribution or arrangement of $m$ distinct or identical balls into $n$ distinct or identical bins with all possible combinations.

learn more… | top users | synonyms

0
votes
2answers
181 views

Probability in ball coloring

You have exactly $n^2$ balls each one of which can be colored in one of $n^2$ ways. That is total colors is $n^2$ but I am not saying all the $n^{2}$ balls are distinctly colored. However assume each ...
3
votes
1answer
61 views

Expected total number of balls in all bins after throwing balls uniformly randomly to bins that have limited capacity

Consider throwing $n$ balls uniformly randomly to $L$ bins. Each bin has capacity $G$, meaning that if a ball is threw to a bin that already has $G$ balls in it, the ball is discarded. Is that ...
2
votes
1answer
102 views

Jee Main 2015 Question. Probabilty

If $12$ identical balls are to be placed in $3$ identical boxes, then the probability that one of the boxes contains exactly $3$ balls is: (1) $22 \times(\frac{1}{3})^{11}$ (2) $\frac{55}{3} \times ...
1
vote
1answer
108 views

About the distribution of balls in bins

Suppose we have $n$ balls and $n$ bins, and consider the following process: at stage $k$, we throw $\ln{n}$ balls into the bins, independently at random. We stop after $n/\ln{n}$ stages, when all ...
0
votes
1answer
72 views

Expected number in b bins with max k balls each, balls in bins question

Suppose we have b bins and each bin could have max k balls. We have sufficient balls and what is the expected number if we need to full all bins? I know the answer when k = 1, the expected number is b ...
3
votes
0answers
31 views

Picking K counters out of K buckets containing NK counters, N of each different colour, up to N in each

This is a generalisation of a question that recently came up while solving a TopCoder problem. Suppose we have N blue counters, N red counters, N white counters, and so forth, K colours in total. We ...
3
votes
0answers
105 views

$m$ balls into $n$ already occupied urns

Assume that there are n urns, $k\in\{1,...,n-1\}$ of which have already at least one ball. $m$ new balls will be thrown into urns. Each of the $m$ balls is thrown randomly and uniformly into $n$ urns. ...
2
votes
0answers
56 views

Expected max load $m$ balls into $n$ bins

If you throw $n$ balls in $n$ bins, it is well known that the expected max load is $\Theta(\lg{n}/\lg{\lg{n}})$. What is the expected max load when you throw $m$ balls into $n$ bins and $m$ ...
2
votes
0answers
84 views

Ways to distribute $25$ distinct balls to $40$ bins with constraints

How many ways there are to distribute $25$ distinct balls to $40$ bins such that: At least one bin will have more than one ball. One and only one bin (not predetermined) will hold exactly ...
2
votes
0answers
75 views

How to estimate pigeonhole principle?

I was thinking about this after my professor mentioned the pigeonhole principle in class. Let's say we have $N$ items and $M$ containers. Here we assume $N > M$. We will randomly place each of the ...
2
votes
0answers
77 views

Maximum bin load for $\alpha n$ balls into $n$ bins

In a paper I am reading the author writes: A standard result concerning balls and bins shows that if we throw at least $\alpha n$ balls into at most $n$ bins, then the maximum bin load is ...
2
votes
0answers
153 views

Modified balls and bins

Assume that we have $n$ balls and $k$ bins. The $n$ balls are are divided into $M$ sets, $\left\{ {{m_i}} \right\}_{i = 1}^M$, where $\sum\limits_{i = 1}^M {\left| {{m_i}} \right|} = n$, $|m_i| \le ...
1
vote
0answers
69 views

Expansion for r-associated Stirling numbers of the second kind

I am looking for a paper or guidance for expanding the r-associated Stirling numbers of the second kind $S_r(n,k)$. $S_r(n,k)$ is the number of ways to partition a set of n objects into k subsets, ...
1
vote
0answers
81 views

Probability of drawing balls with different colours

In a jar of balls with different colours, can we find a general probability distribution of having n distinct colours with N number of balls grabbed ? Assuming that any colours have an equal chance to ...
1
vote
0answers
102 views

n bins, m balls and m>n: Probability of at least r bin containing exactly k balls.When bins are numeret from 1…n and ball is equale.

I want to calculate this probability .In this question $N$ bins, $m$ balls: Probability of any bin containing *exactly* $k$ balls. calculate this but I can not understand this calculation.To be more ...
1
vote
0answers
45 views

Distribution of maximum/minimum proportion in a sampling process

I am facing something that can be explained as a balls & urns problem. Suppose you have $B$ black and $W$ white balls inside an urn. They are randomly chosen, one by one, without replacement, and ...
1
vote
0answers
94 views

Occupancy distribution bounds for $k$ balls in $m$ bins

Suppose we throw $k$ (distinct) balls into $m$ (distinct) bins, and let $B$ count the number of non-empty bins. I am interested in lower bounds on $B$. More precisely, I wish to bound from above the ...
1
vote
0answers
76 views

Balls and bins question with nlogn balls and n bins.

The question: Suppose we randomly drop nlogn balls into n bins. Give an upper bound on the expectation of the maximum number of balls in any bin. How would this be done? I believe the answer is well ...
1
vote
0answers
176 views

The probability of two balls going into the same bin

Suppose I have n bins and n balls with label on them. What would be the probability that I throw the i th ball into the same bin as the j th ball? Is it just 1/n because there is a probability of 1/n ...
1
vote
0answers
88 views

Poisson Distribution?

There exists 1000 boxes. These boxes are randomly filled with balls. How many balls are required in order that only 1 in 100 boxes are left empty? This sounds like a Poisson distribution problem to ...
1
vote
0answers
83 views

balls and bins: the first time when max-loaded is less than twice min-loaded

We have $n$ bins, in each step we throw a ball in a bin chosen uniformly and independently from the $n$ bins we have. We repeat the process $k$ times. Let $B_k$ be the number of balls in ...
0
votes
0answers
22 views

Given $d>8$ boxes and $n$ balls. . What is $P(A \cup B \cup C)$?

Given $d>8$ boxes and $n$ balls. Consider event $A$=boxes numbered $1,2,3,4$ receive 0 balls.$B=3,4,5,6$ receive 0 balls, $C=5,6,7,8$ receive zero balls. What is $P(A \cup B \cup C)$? ...
0
votes
0answers
58 views

Possible combinations of N different balls in M identical bins with the same capacity L

For a distribution center I am interested in the number of possible combinations to put N different boxes (all the same size but different content) into M equal bins (containers) with capacity L, with ...
0
votes
0answers
18 views

Matching Question - a derivative of the birthday problem with two types

I am trying to calculate the expected number of matched trades given b buy orders and s sell orders, each on one of N underlying products. I think this can be cast as a balls-in-bins problem: If I ...
0
votes
0answers
132 views

Standard problem of Balls and Bins

A general classification of balls and boxes problems in combinatorics in 12 ways. There are 12 categories since 1. Balls may be distinguishable or indistinguishable; 2. Boxes may be distinguishable or ...
0
votes
0answers
102 views

balls in bins — waiting time until $k$ bins are occupied

Consider the classic balls in bins problem: we throw balls one by one into $n$ bins independently and uniformly. Define $\tau(k)$ for $1 \le k \le n$ to be the number of balls we have thrown until $k$ ...
0
votes
0answers
199 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 ...