Question

Nine sales representatives for a company are to be chosen at random to participate in a training program. The company has fifteen sales​ representatives, three in each of five regions. What is the probability that the nine sales representatives chosen to participate in the training program will be from only three of the five ​regions?

Answer 1

Total number of ways to select 9 sales representatives out of 15 = ¹⁵C₉ = 15! / (9! * (15 - 9)!) = 5005

Total number of ways to choose 3 regions out of 5 = ⁵C₃ = 5! / (3! * (5 - 3)!) = 10

P(nine sales representatives will be from only three of the five ​regions) = ⁵C₃ * ³C₃ * ³C₃ * ³C₃ / ¹⁵C₉

                     = 10 * 1 * 1 * 1 / 5005

                     = 2 / 1001 or 0.002