1. Refer to Exercise 5. How many different sequences are possible?

In the World Series, the American League team ("A") and the National League team ("N") play until one team wins four games. Each sequence of winners can be designated by a sequence of As and Ns. For instance, NAAAA means the National League won the first game and lost the next four games. In how many ways can a series end in seven games? Six games?

2. A football team plays 11 games. In how many ways can these games result in five wins, five losses, and one tie?

3. A chess master plays 15 games. In how many ways can these games result in 10 wins, 2 losses, and 3 draws?