Concept explainers
Elimination Tournaments The following diagram illustrates a 16-team tournament bracket, in which the 16 participating teams are arranged on the left under Round 1 and the winners of each round are added as the tournament progresses. The top team in each game is considered the “home” team, so the top-to-bottom order matters.
To seed a tournament means to select which teams to play each other in the first round according to their preliminary ranking. For instance, in professional tennis and NCAA basketball the seeding is set up in the following order based on the preliminary rankings: 1 versus 16, 8 versus 9, 5 versus 12, 4 versus 13, 6 versus 11, 3 versus 14, 7 versus 10, and 2 versus 15.48 Exercises 37–40 are based on various types of elimination tournaments. (Leave each answer as a formula.)
In a randomly chosen seeding of a 16-team tournament, what is the probability that the top-ranked team plays the bottom-ranked team, the second-ranked team plays the second-lowest ranked team, and so on? [HinT: See Exercise 65 in Section 7.4.]
Trending nowThis is a popular solution!
Chapter 7 Solutions
Finite Mathematics
- Batting Order A baseball coach is creating a nine-player batting order by selecting from a team of 15 players. How many different batting orders are possible?arrow_forwardChoosing Officers From a pool of 12 candidates, the offices of president, vice-president, secretary, and treasurer need to be filled. In how many different ways can the offices be filled?arrow_forwardKidney Donors A patient with end-stage kidney disease has nine family members who are potential kidney donors. How many possible orders are there for a best match, a second-best match, and a third-best match?arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageAlgebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning