Andy and Marjorie are playing tennis. The points system is as follows: there are two conditions for a player to win a game: 1) A player must reach four points in that game before their opponent. So for example, if Andy wins four out of the first five points, then he wins 4-1. 2) A player must have at least two more points in that game than their opponent. So for example, if the score is 3-3 and then Andy wins a point, then the score is 4-3 to Andy but the game isn't over. If Andy wins the next point, then he wins the game 5-3; otherwise, the score is 4-4, and again a player must win two points in a row to win the game. When the score in a game is tied at 3-3 (or 4-4, or 5-5, and so on), it is called 'deuce'. To win a set, a player must win six games before their opponent and as with games, this must be by a difference of two. So for example if Marjorie wins 6 out of the first 8 games, she wins the set 6-2. Unlike games, however, sets do not go on indefinitely. You may assume for now that once the set reaches 6-6, it ends in a tie (so no 'tiebreaker'). i. How many ways are there for the score in a game to reach 4-4 from a starting score of 0-0?
Andy and Marjorie are playing tennis. The points system is as follows: there are two conditions for a player to win a game: 1) A player must reach four points in that game before their opponent. So for example, if Andy wins four out of the first five points, then he wins 4-1. 2) A player must have at least two more points in that game than their opponent. So for example, if the score is 3-3 and then Andy wins a point, then the score is 4-3 to Andy but the game isn't over. If Andy wins the next point, then he wins the game 5-3; otherwise, the score is 4-4, and again a player must win two points in a row to win the game. When the score in a game is tied at 3-3 (or 4-4, or 5-5, and so on), it is called 'deuce'. To win a set, a player must win six games before their opponent and as with games, this must be by a difference of two. So for example if Marjorie wins 6 out of the first 8 games, she wins the set 6-2. Unlike games, however, sets do not go on indefinitely. You may assume for now that once the set reaches 6-6, it ends in a tie (so no 'tiebreaker'). i. How many ways are there for the score in a game to reach 4-4 from a starting score of 0-0?
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