New car owners were asked to evaluate their experiences in b

New car owners were asked to evaluate their experiences in buying a new car during the past 12 months. In the survey, the owners indicated they were most satisfied with their experiences at the following three dealers (in no particular order): Subaru, Honda, and Buick. Assuming that each set of rankings is equally likely, what is the probability that owners ranked Subaru first?

Solution

Let S : Subaru

H : Honda

B : Buick

{ SHB , SBH, HSB, HBS, BHS, BSH}

Total no of ways in which the 3 cars can be ranked = 3! = 6

No of ways in which Subaru can be ranked 3rd = 2

Prob ( owners ranked Subaru third) = (2/6) = (1/3)