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6
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Probability that the maximum number of dice with the same face is k
Let say we have $N$ dice with 6 faces. I'm asking my self, what is the probability that the maximum number of dice with the same face is $k$?
In more precise terms, what is the size of this set?
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1
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2
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59
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How to rigorously interpret and transform "equal chance" in different ways?
Put $100$ identical balls into $10$ identical boxes in a way that each ball enters each box with an equal chance. What's the probability that no box is empty?
I have solved it but like to discuss ...
- 2,036
1
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0
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Number theoretic calculation of probability problem involving partitions.
This question asks for a specific miscalculation of how large chance that I get at least one call every day of the week if I in total get 12 calls during a week.
If we instead consider the question ...
- 26.1k
3
votes
1
answer
337
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Add together numbers to make final number?
I have this problem where I want to add some numbers together to make a final number. I ask how many ways are there to make this final number using exactly k numbers? Here is the condition:
(1) The ...
3
votes
1
answer
183
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How to calculate the distribution of the last digit of an integer partition?
Definition
Let's denote $P(n,k)$ represents the set of ordered partitions of integer $n$ into $k$ parts. For example, $P(5,3)=\{(1,1,3),(1,2,2),(1,3,1),(2,1,2),(2,2,1),(3,1,1)\}$
(there is another ...
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6
votes
1
answer
234
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When is the sum of first $n$ numbers equal to the sum of the next $k$ numbers?
When is the sum $1+2+\cdots + n = (n+1) + (n+2) + \cdots +(n+k)$?
The easiest solution $(n,k)$ is $(2,1)$. For example, $1+2 = 3$. Do any others exist?
Roots of $(n+k)^2 + (n+k) = 2n^2 +2n$ give ...
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