So, the problem I found goes like this:
You have $n$ different numbers, numbered from $ 1 $ to $n$. You can randomly choose $m$ (different) of them. The computer also randomly selects $m$ (different) of them. If you and the computer have exactly $k$ common numbers, then you win a certain amount of money.
The problem asks us to find the probability of winning.
I have solved some easier problems involving probabilities. But here, the only thing I could think of was that the probability for a certain sequence of $m$ numbers to emerge is:
$$ \frac{1}{\dbinom{n}{m}} $$
How do you solve it? I'm on my way of getting used to this type of problems and I could really use some help.