This procedure is used to break ties in games in the championship round of the World Cup soccer tournament. Each team selects five players in a prescribed order. Each of these players takes a penalty kick, with a player from the first team followed by a player from the second team and so on, following the order of players specified. If the score is still tied at the end of the $10$ penalty kicks, this procedure is repeated. If the score is still tied after $20$ penalty kicks, a sudden-death shootout occurs, with the first team scoring an unanswered goal victorious.
- How many different scoring scenarios are possible if the game is settled in the first round of $10$ penalty kicks, where the round ends once it is impossible for a team to equal the number of goals scored by the other team?
- How many different scoring scenarios for the first and second groups of penalty kicks are possible if the game is settled in the second round of $10$ penalty kicks?
- How many scoring scenarios are possible for the full set of penalty kicks if the game is settled with no more than $10$ total additional kicks after the two rounds of five kicks for each team?