Two players A and B play a series of games of badminton. The player, who wins 5 games first, wins the series. Assuming that no game ends in a draw, the number of ways, in which player A wins the series is __________.

Step-by-step solution

Player A wins the series if A wins 5 games before B wins 5 games. The series can last for a minimum of 5 games and a maximum of 9 games. If player A wins the series in exactly n games, then A must win the n -th game, and A must win exactly 4 out of the first n-1 games. The number of ways this can happen is given by ^ n-1 C₄ . The possible values for n are 5, 6, 7, 8, and 9 . Total number of ways for A to win the series is the sum of the number of ways A can win in 5, 6, 7, 8, or 9 games: Total ways = ⁴C₄ + ⁵C₄ + ⁶C