There are four distinct types of human blood denoted by O, A, B and AB. Suppose that these types occur with the following frequencies: 0.45, 0.40, 0.10, 0.05, respectively. If 20 people are chosen at random, what is the probability that:
i) All 20 people have blood of the same type?
ii) Nine people have blood type O, eight of type A, two of type B and one of type AB?