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 $S=s$