PART 2 - THE LURE OF GULLTOWN After much wheeling and dealing (and some tricking) all the seats on the ship are filled, and at least four contestants from each of the twelve houses end up boarding the ship. However, on their way to King's Landing, the ship lands in Gulltown for reprovisioning. Gulltown is a prosperous town in a beautiful natural setting and four of the contestants decide to settle down in Gulltown instead of continuing to King's Landing and participating in the tournament. d) (7 marks) Given that at least four contestants out of the six for each of the twelve houses end up boarding the ship, and that the ship is at full capacity, how many different house configurations of the passengers could there be on the ship? (Here is an example of a configuration: 6 TAR, 5, Lan, 4 STA, 4 TYR, 4 BAR, 6 MAR, 5 ARR 6 TUL, 5 GRE, 6 BOL, 4 FRE). Explain your answer. e) (3 marks) In how many different ways can the twelve great houses participating in the tournament be affected by the four defections in Gulltown? (in other words in how many different ways can the twelve houses lose these four contestants?). Explain your answer. Note that this question is independent of a) and can be answered before a). It is much easier than a) so you may want to start here. PART 2 - THE LURE OF GULLTOWN After much wheeling and dealing (and some tricking) all the seats on the ship are filled, and at least four contestants from each of the twelve houses end up boarding the ship. However, on their way to King's Landing, the ship lands in Gulltown for reprovisioning. Gulltown is a prosperous town in a beautiful natural setting and four of the contestants decide to settle down in Gulltown instead of continuing to King's Landing and participating in the tournament. d) (7 marks) Given that at least four contestants out of the six for each of the twelve houses end up boarding the ship, and that the ship is at full capacity, how many different house configurations of the passengers could there be on the ship? (Here is an example of a configuration: 6 TAR, 5, Lan, 4 STA, 4 TYR, 4 BAR, 6 MAR, 5 ARR 6 TUL, 5 GRE, 6 BOL, 4 FRE). Explain your answer. e) (3 marks) In how many different ways can the twelve great houses participating in the tournament be affected by the four defections in Gulltown? (in other words in how many different ways can the twelve houses lose these four contestants?). Explain your answer. Note that this question is independent of a) and can be answered before a). It is much easier than a) so you may want to start here