Apologies if this seems like a basic question, but I haven't been able to find a clear answer in my textbook or online.
The original problem;
Please determine the probability of finding exactly 3 defective and 7 non-defective items if we pick 10 items from a lot consisting of 20 defective and 80 non-defective (without replacement).
From what I've managed to find, the probability for a binomial distribution would've been $nPk*(p^k)*(1-p)^{n-k}$, but this seems to only apply in cases where there is a consistent probability across trials.
I tried $100P10 * (\frac{20}{100})(\frac{19}{99})(\frac{18}{98})(\frac{80}{97})(\frac{79}{96})...(\frac{73}{90})$ but I got a number in the tens of billions instead of anything that could reasonably be a probability.
Any advice on how I should change the binomial distribution to make it function with the problem?