Originally Posted by

**mbaboy** The four major bloodtypes in the US are A (42%), B (10%), AB (4%) and O (44%) where the percentages denote the proportion of the population.

If four people are picked at random, let P(k) be the chance that there are exactly k different bloodtypes among the four people. What is the probability P(k) for k = 1,2,3,4?

Now theoretically I can do this, but it would take me half an hour. Is there a simpler way of thinking about this? P(1) is easy to compute, so maybe there is a way to build on that to get P(2) and so on. Any help?