A local high school soccer team has 20 players. However, only 11 players play at any given time during a game. In how many ways can the coach choose 11 players To be more realistic, the 11 players playing a game normally consist of 4 midfielders, 3 defend­ ers, 3 attackers and 1 goalkeeper. Assume that there are 7 midfielders, 6 defenders, 5 attackers and 2 goalkeepers on the team 2. In how many ways can the coach choose a group of 4 midfielders, 3 defenders, 3 attackers and 1 goalkeeper? 3. Assume that one of the defenders can also play attacker. Now in how many ways can the coach choose a group of 4 midfielders, 3 defenders, 3 attackers and 1 goalkeeper?

Computer Networking: A Top-Down Approach (7th Edition)
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Author:James Kurose, Keith Ross
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Discrete Mathematics.Combinations and Permutations. 

(5,10,10): Soccer

A local high school soccer team has 20 players. However, only 11 players play at any given time during a game.

  1. In how many ways can the coach choose 11 players

To be more realistic, the 11 players playing a game normally consist of 4 midfielders, 3 defend­ ers, 3 attackers and 1 goalkeeper. Assume that there are 7 midfielders, 6 defenders, 5 attackers and 2 goalkeepers on the team

2. In how many ways can the coach choose a group of 4 midfielders, 3 defenders, 3 attackers and 1 goalkeeper?

3. Assume that one of the defenders can also play attacker. Now in how many ways can the coach choose a group of 4 midfielders, 3 defenders, 3 attackers and 1 goalkeeper?

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