A ship is carrying 30 travelers from various great houses on along sea voyage from Braavos to King’s Landing where they willparticipate in the Game of Thrones: 5 are from HouseTargaryen(TAR), and 5 from House Lannister (LAN) 4 are from HouseStark (STA) and 4 from House Tyrell (TYR) 3 are from HouseBaratheon (BAR) and 3 from House Martell (MAR) 1 from each of thefollowing houses: House Arryn (ARR), House Tully (TUL), HouseGreyjoy (GRE), House Bolton (BOL), House Frey (FRE), HouseMormont(MOR) You are now asked to evaluate probabilities relatingto this voyage. Part 1 - Leaving the Ship Only 9 of the 30travelers will end leaving the ship when they reach King’s Landing.Based solely on the number of travelers per house, what is theexpected value of the number of travelers from LAN leaving theship? the number of travelers from STA leaving the ship? the numberof travelers from BOL leaving the ship? Part 2 - Game of ThronesThe following 9 competitors end up leaving the ship andparticipating in the Game of Thrones: 3 from TAR, 2 from LAN, 2from STA, 1 from GRE' and 1 from MAR. At the end of the Game ofThrones,only 3 of the 9 competitors will win titles: 1 will win theIron Throne (I), 1 will end up being the Hand of the King (H) 1will be the King of the North (N) Nobody can win more than onetitle. In how many different ways can these 3 titles be distributedamong the 9 competitors? In how many different ways can these 3titles be distributed among the 5 participating houses? (in otherwords we are asking you to figure out how many possiblecombinations of titles by houses there can be.) Your answer shouldnot be derived by listing all the possibilities one by one. Insteadyou should derive your answer by reasoning with known formulas forpermutations and combinations. Based solely on the number ofcompetitors per house and not on their ability to wield a sword,axe, or their ability to devise a cunning plan, what is theprobability that GRE will win at least one title? Based solely onthe number of competitors per house and not on their ability towield a sword, axe, or their ability to devise a cunning plan, whatis the probability that LAN will win at least one title? Basedsolely on the number of competitors per house and not on theirability to wield a sword, axe, or  ability to devise acunning plan, what is the probability that TAR will win at leastone title?
