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Refer to Exercise 2.46. If 2n teams are to be assigned to
Chapter 2, Problem 47E(choose chapter or problem)
Refer to Exercise 2.46. If \(2n\) teams are to be assigned to games 1, 2, . . . ,\(n\), in how many ways can the teams be assigned to the games?
Questions & Answers
QUESTION:
Refer to Exercise 2.46. If \(2n\) teams are to be assigned to games 1, 2, . . . ,\(n\), in how many ways can the teams be assigned to the games?
ANSWER:
Step 1 of 2
In how many ways can the teams be assigned to the games, if 2n teams are to be assigned to games 1, 2, ........, n.
Reference: In how many ways can the teams be assigned to the games, if ten teams are playing in a basketball tournament. in the first round, the teams are randomly assigned to games 1, 2, 3, 4, 5.
The number of unordered subsets of size r chosen (without replacement) from n available object is
……………..(1)
This is also called a combinations theorem.
Given numbers of teams playing n = 10 , a number of games = 5.
Because only two teams can participate in one game, we can write r = 2
Hence there are (10, 2) ways to choose two teams for the first game, (8, 2) for the second game, (6, 2) for the third game, etc.
So, there are ways to assign the ten teams for five games.
Same way we have given here,
Number of teams = 2 n , and number of games = 1, 2, ........, n.
Because only two teams can participate into one game, we can write r = 2
Hence there are (2n, 2) ways to choose two teams for the first game, (2n ? 2, 2) for the second game, (2n-4, 2) for the third game, etc.