Use counting arguments from the preceding chapter. The following seven teams will be participating in Urban University's hockey intramural tournament: the Independent Wildcats, the Phi Chi Bulldogs, the Gate Crashers, the Slide Rule Nerds, the Neural Nets, the Edmontons Eulers, and the City Slickers. Prizes will be awarded for the winner and runner-up. (a) Find the cardinality n(S) of the sample space s of all possible outcomes of the tournament. (An outcome of the tournament consists of a winner and a runner- up.)
(b) Let E be the event that the City Slickers are runners-up, and let F be the event that the Independent Wildcats are neither the winners nor runners-up. Express the event EUF in words. EUF is the event that the City Slickers are runners-up, and the Independent Wildcats are neither the winners nor runners-up. EUF is the event that either the City Slickers are not runners-up, or the Independent Wildcats are neither the winners nor runners-up. EUF is the event that either the City Slickers are not runners-up, and the Independent Wildcats are not the winners or runners-up. EU F is the event that either the City Slickers are runners-up, or the Independent Wildcats are neither the winners nor runners-up. EUF is the event that the City Slickers are not runners-up, and the Independent Wildcats are neither the winners nor runners-up. Find its cardinality.