The City Housing Authority has received 50 applications from

The City Housing Authority has received 50 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 specific qualified applicant will be selected for one of these apartments. (Round your answer to three decimal places.) Two specific qualified applicants will be selected for apartments on the same side of town. (Round your answer to five decimal places.)

Solution

a. For a particular qualified applicant to be selected, number of ways = 49C9 (As given he is chosen, the other 9 winners will be chosen from 49 remaining applicants)

Total number of ways of selecting winners = 50C10

Probability = 49C9 / 50C10 = 0.200

b. Number of ways in which 2 qualified applicants will be selected for apartments on same side = 2*48C3*45C5

(As fixing the 2 applicants on 1 side, 3 out of 48 will be chosen for that side, and 5 out of remaining 45 for the other side, 2 is multiplied for north and south)

Total number of ways = 50C5*45C5

Probability = 2*48C3*45C5 / 50C5*45C5 = 0.016