What's a distribution that is like the hypergeometric, finite population N but you
a)have more than 2 types, say 3, each with their own probability p_n and type_population size(x type As with p_1 to appear, y type Bs with p_2 to appear, z type Cs with p_3 to appear)
b)Replace failures in the population(if you search for As and draw any other you reinsert them into the population)

For a) is it logical to just multiply the type_population_size with each corresponding p_n and then treat them as equally possible?

What's the probability mass function that you draw X times type As in K tries?