Refer to Exercise 2.46. If 2n teams are to be assigned to

Chapter 2, Problem 47E

(choose chapter or problem)

Get Unlimited 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?

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.

Add to cart


Study Tools You Might Need

Not The Solution You Need? Search for Your Answer Here:

×

Login

Login or Sign up for access to all of our study tools and educational content!

Forgot password?
Register Now

×

Register

Sign up for access to all content on our site!

Or login if you already have an account

×

Reset password

If you have an active account we’ll send you an e-mail for password recovery

Or login if you have your password back