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(d) Show that for all integers n > 1 S(n, 1) = 1 = S(n,n), then, using the above relation (or otherwise), show that S(4,2) = 7. (e) A game is played by 5 people - Brian, Malcolm, Phil, Angus and Cliff. The game has 3 rounds. In each round of the game, players must divide into 2 teams. A team must consist of at least 2 people. In each round the teams must be different. Below is one example of a composition of teams across all three rounds: Round 1 Round 2 Round 3 Team 1 Team 2 Team 1 Team 2 Team 1 Team 2 Cliff Brian Cliff Angus Cliff Angus Angus Phil Brian Malcolm Brian Malcolm Malcolm Phil Phil What is the total number of compositions of teams across all three rounds of the game?

(d) Show that for all integers n > 1 S(n, 1) = 1 = S(n,n), then, using the above relation (or otherwise), show that S(4,2) = 7. (e) A game is played by 5 people - Brian, Malcolm, Phil, Angus and Cliff. The game has 3 rounds. In each round of the game, players must divide into 2 teams. A team must consist of at least 2 people. In each round the teams must be different. Below is one example of a composition of teams across all three rounds: Round 1 Round 2 Round 3 Team 1 Team 2 Team 1 Team 2 Team 1 Team 2 Cliff Brian Cliff Angus Cliff Angus Angus Phil Brian Malcolm Brian Malcolm Malcolm Phil Phil What is the total number of compositions of teams across all three rounds of the game?

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 32EQ
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(d) Show that for all integers n >1 S(n,1)= 1 = S(n,n), then, using the above relation (or otherwise), show that S(4,2) = 7. (e) A game is played by 5 people - Brian, Malcolm, Phil, Angus and Cliff. The game has 3 rounds. In each round of the game, players must divide into 2 teams. A team must consist of at least 2 people. In each round the teams must be different. Below is one example of a composition of teams across all three rounds: Round 1 Round 2 Round 3 Team 1 Team 2 Team 1 Team 2 Team 1 Team 2 Cliff Brian Cliff Angus Cliff Angus Angus Phil Brian Malcolm Brian Malcolm Malcolm Phil Phil What is the total number of compositions of teams across all three rounds of the game?
Transcribed Image Text:(d) Show that for all integers n >1 S(n,1)= 1 = S(n,n), then, using the above relation (or otherwise), show that S(4,2) = 7. (e) A game is played by 5 people - Brian, Malcolm, Phil, Angus and Cliff. The game has 3 rounds. In each round of the game, players must divide into 2 teams. A team must consist of at least 2 people. In each round the teams must be different. Below is one example of a composition of teams across all three rounds: Round 1 Round 2 Round 3 Team 1 Team 2 Team 1 Team 2 Team 1 Team 2 Cliff Brian Cliff Angus Cliff Angus Angus Phil Brian Malcolm Brian Malcolm Malcolm Phil Phil What is the total number of compositions of teams across all three rounds of the game?
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