Maybe you could help me with the following problem.
Given a series of incremental numbers that is split in two, so $s = 1, 2, 3, ..., n_1$, $n_1 + 1, n_1 +2 ,..., n_2$. Also given a integer number $0 < x < n_2$.
Now take a random combination of $x$ numbers out of $s$ (so without replacement and order does not matter).
- What is the probability that the random combination contains all numbers between and including $1$ and $n_1$? The combination might include numbers larger than $n_1$.
- What is the probability that the random combination contains all numbers between and including $n_1 + 1$ and $n_2$? The combination might include numbers smaller than or equal to $n_1$.
Both probabilities would be ideally expressed in terms of $n_1, n_2$ and $x$.
I hope I expressed the problem clearly, otherwise I can add more information.