It is October when thoughts turn to baseball and the Red Sox winning the World Series! (Maybe next year. 1. The world series is played by the final two teams not eliminated in the playoffs. The team that wins the world series is the first team to win 4 games. As soon as one team or the other has won 4 games, the series is over and no more games are played. Explain why the world series can not go more than 7 games. What mathematical principle are you appealing to in your answer? 2. If the Red Sox play in the World Series, in how many ways can they win the World Series? Each way is defined be a sequence of Wins (W) or Losses (L). Possible winning sequences include WWWW, WLWWLW, and LLLWWWW. Remember that the World Weries can go at most 7 games and no more games are played after one of the two teams wins 4 games. For full credit, state your answer in the form of a concise mathematical expression and then reduce your answer to a single integer. (No credit is given for simply enumeratiog all possibilities.) 3. On a baseball team there are 9 player positions, designated 1-9. The manager decides the batting order of the nine players. This is sometimes called the batting lineup or simply the lineup. How many lineups have the 6 infielders {1, 2, 3, 4, 5, 6} batting together (in any order) and the 3 outfielders {7, 8,9} batting together in any order. One possible batting sequence is 8 - 7 - 9 = 1 - 6 - 2 -+ 5 + 3 -+ 4 and another is 5 -+ 6 - 3 - 4 - 1 - 2= 9-+ 8 - 7. A concise mathematical expression suffices for an answer but be sure to explain your