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Same question as "Distribution of $N$ balls numbered $1$ to $N$ with replacement", but without replacement:

An urn contains $N$ balls numbered $1,2,3,...,N$.

I draw at random $n$ balls, one by one WITHOUT replacement.

Let $X$ the smallest number, the largest $Y$ and $S$ the sum of all the $n$ numbers

How to compute:

  • the probability $P(X=x,Y=y)$ that $X=x$ AND $Y=y$
  • the probability that $S=s$
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    perhaps you'd better merge these questions2011-05-11
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    @LeilaHatami And yet another useless edit to a 6 years old question. Well done.2017-03-20
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    @Did Sure you cannot find more productive ways of contributing to the site?2017-03-20

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