During autumn 2001, there was a highly publicized outbreak of anthrax cases among U.S. Postal Service workers. In Chance (Spring 2002), research statisticians discussed the problem of sampling mailrooms for the presence of anthrax spores. Let x equal the number of mailrooms contaminated with anthrax spores in a random sample of n mailrooms selected from a population of N mailrooms. The researchers showed that the probability distribution for x is given by the formula

where k is the number of contaminated mailrooms in the population. (In section 4.4 we identify this probability distribution as the hyper geometric distribution.) Suppose N = 100, n = 3, and k = 20.
a. Find p(0).
b. Find p(1).
c. Find p(2).
d. Find p(3).

(N-k p(x) =