4. A rural county has nine towns in it. Each of these towns has three electrical transformers (so there are 27 total transformers). Suppose that the power company needs to take 12 of the transformers offline for emergency maintenance. Assume that the 12 to be taken offline are randomly chosen from among the 27 possible transformers. Assume also that if (and only if) one or more of the transformers in a given town are taken offline, the town will lose power. (a) How many different subsets of 12 of the transformers are there that might be taken offline? (b) One of the towns is named Conrad. How many of the subsets from (a) are such that none of the 12 transformers chosen are from Conrad? (c) What is the probability that Conrad does not lose power? (d) What is the expected number of towns that do not lose power