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The City Housing Authority has received 75 applications from qualified applicants for ten low-income apartments. Five of the apartments are on the north side of town, and five are on the south side. If the apartments are to be assigned by means of a lottery, find the following probabilities. (a) A specific qualified applicant will be selected for one of these apartments. (Round your answer to three decimal places.) (b) Two specific qualified applicants will be selected for apartments on the same side of town. (Round your answer to five decimal places.)

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You are given the City Housing Authority with 75 applications from qualified applicants for ten low-income apartments. Five of the apartments are on the north side of town, and five are on the south side. The condition is that the apartments are to be assigned by means of a lottery and the following questions were asked
(a) A specific qualified applicant will be selected for one of these apartments.
(b) Two specific qualified applicants will be selected for apartments on the same side of town. 

This problem is an example of combination of ways. There are 75C2 position pairs for a [articular pair of names to be placed in. About 5C2 of these position pairs are selected in the north and 5C2 are selected in the south. So the probability that a specific pair are both north or both south is

(5C2 + 5C2)/(75C2) = (10 + 10)/2775
= 4/555

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