Professional sports teams commonly end their seasons with a championship between two teams. The series ends when one team has one 4 games and so must last at least 4 games and at most 7. How many different sequences of game winners are there in which the game ends in 5 games? 6 games? 7 games?
My attempt involved noticing that there are two teams, and realizing that if 5 games have been played, one team must have won 4 and the other won 1 game. So I tried seeing how many different ways that one team can win 4 games and the other team can win 1, but I cant seem to get the correct answer.