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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Probability of 3rd ball being blue given at least 1 blue previously
I have a bin with $5$ blue and $10$ red balls. I take out $2$ and at least one is blue. I then take a 3rd.
What is the probability that the 3rd ball is blue?
I understand I likely need conditional ...
- 51
0
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Distribution of passengers into distinct cars
In four cars, 16 passengers randomly enter. What is the probability of the following events:
a) 4 passengers enter the first car
b) each car receives exactly 4 passengers
I am trying to decide between ...
- 3
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Distinguishable objects into distinguishable boxes.
So here is the problem. We have $500$ fans of which $200$ Americans,$150$ Polish, $100$ Italians and $50$ French. They are about to travel to Paris for the start of the Olympic games with 5 different ...
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Probability of no empty bins when $n$ balls go into $3$ bins
I'm a bit unsure what's wrong with my reasoning here:
So we have $n$ balls, and want to place them into 3 bins, and we want the probability that $0$ bins are empty.
Numerator: number of ways that $0$ ...
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Numbered Sets of Balls in Bins
For any prime power $N$, suppose we have $N^2+N+1$ indistinguishable bins, $N^2+N+1$ distinct people, and each person has $N+1$ indistinguishable balls.
Each person throws all of their balls into a ...
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1
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Putting $k$ balls in n urns, which are grouped into $r$ sets.
Suppose I have $k$ balls, $n$ urns, and the urns are grouped into $2r+1$ sets where each set contains $\frac{n}{2r+1}$ urns. Assume that $n$ is a multiple of $2r+1$. (The choice of $2r+1$ rather than $...
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No adjacent empty boxes with PIE
*PIE = inclusion-exclusion
How many ways are there to distribute 10 balls into 5 distinct boxes such that no two adjacent boxes are empty?
Note: the same question statement.
I believe the question ...
- 127
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number of possibilities to distribute k balls in 2n boxes with condition
I'm trying to find the number of possibilities to distribute $k$ balls to $2n$ boxes such that for every $i$ between $1$ and $n$ the sum of the balls in the $i$ box and the $n+i$ box isn't equal to $6$...
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In how many ways it is possible to take out balls from the basket , such that will take out at least one from each color?
The question:
In a basket there are $20$ black balls, $15$ white balls and $18$ red balls. All balls with the same color are identical to each other. In how many ways it is possible to take out balls ...
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Number of ways of distributing white and black balls into bowls
This is a self-answer question that repeats this posted question that the original poster deleted themself. I regard the math problem as interesting enough to warrant posting.
I will be very ...
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Probability of empty bin, where the number of balls is based on another game...
Came across this interesting question:
We are given $j$ balls. We put them into bins labelled $1$, $2$, and $3$ at random. We want to calculate P(all bins have at least a ball).
The approach I'm using ...
- 625
0
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77
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Chance that a group of $n$ people collectively have a missing birthday.
Suppose there is a city with $n$ residents, what is the probability that there is some day in the year at which none of them have their birthday?
In other words, suppose we divide $n$ balls into $k=...
- 2,305
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$m$ distinct boxes and $n$ distinct balls probability problem [closed]
I have looked at similar questions, however I could not find an answer to my specific problem. The problem is the following: If I have $m$ distinct boxes and $n$ distinct balls, what is the ...
2
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1
answer
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In how many ways can 20212022 identical balls be arranged in 2022 different bins [with conditions]?
The problem goes like this:
in how many ways can 20212022 identical balls be arranged in 2022 different bins so that the number of bins with exactly 4 balls is 3, with exactly 7 balls is 4 (2), and ...
3
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Balls are pulled and distributed randomly into the boxes. What is the probability that in no boxes there will be balls of the same color?
Full Question: The pool of 100 balls contains 20 pink balls, 10 yellow balls, 20 purple balls, 15 indigo balls and 35 green balls. We randomly pull 10 balls out of 100 and randomly distribute them ...
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