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 topto- 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 an 8-team tournament, what is the probability that each team plays a team with adjacent ranking?
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
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 topto-
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 an 8-team tournament,
what is the probability that each team plays a team with
adjacent ranking?
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