Given a population of m, that has k subpopulations of n1, n2, ...., nk elements each, and a sample size r:
How can we calculate the amount of different subsets with r of the m elements, ignoring the order of the elements and considering all the elements of the same subpopulation unrecognizable form each other?

For example: m=6, r=4, k=3, n1=1, n2=2, n3=3 ((ABBCCC))
The possible subsets are 5:
ABBC, ABCC. ACCC, BBCC, BCCC

Bros please i dont now if there is method for this because it certainly asnt in my classes. I tried this but it doesnt werk