Example 3: Team A and Team B each send out 7 players to participate in a Go broadcast tournament according to a pre-arranged order. Both sides start with Player 1 competing, the loser is eliminated, and the winner then competes with the next player (Player 2) from the losing side... until all players from one side are eliminated. The other side wins. This forms a competition process. How many different competition processes can occur?
Team A players are represented by black balls, and Team B players are represented by white balls ○. Each match process in the tournament corresponds to a permutation of 7 - and 7 ○, which can be verified to be a one-to-one mapping, such as the permutation
$0 \bigcirc 000000 \bigcirc 0000$

indicating a match process: the lead player of Team A lost, the 2nd player of Team A defeated the 1st and 2nd players of Team B but lost to the 3rd player of Team B, the 3rd and 4th players of Team A lost consecutively, the 5th player of Team A defeated the 3rd and 4th players of Team B but lost to the 5th player of Team B, the 6th player of Team A consecutively defeated the 5th, 6th, and 7th players of Team B. Team A won the match. The 7th player of Team A did not play. Conversely, each match process uniquely corresponds to a permutation of 7 - and 7 ○, so there are a total of $C_{44}=3432$ different match processes.