How would I calculate the following:
Chance for getting $M$ samples from each of $N$ Groups given $S$ samples when drawing one by one with replacement.
I want to plot the probability for $M=1$ given Sample sizes $S =1:100$ for $N=10$ Grops.
I draw one sample and note the group it belong to. $N=10$ groups. (assume equal size of each group) I continue to draw samples $S=50$ times and would now like to know, what is the chance I get more or $M=1$ from each of the 10 groups.
I want to do it generic for $N,M,S$
Does it make sense?