A lake contains 4 types of fish ,Suppose each fish caught is equally likely to be any one of these types.

Let Y be the number of fish that need ti be caught in order to obtain at least one of each type.

Q1:What is the distribution of Y?

Q2:Give an interval(a,b)such that P(a<Y<b)>0.9

i think it like "negative binominal"

but the probility of each time is difference,

so, anyone help me?