Question

In a competition between players X and Y, the first player to win three games in a row or a total of four games wins. How many ways can the competition be played if X wins the first game and Y wins the second and third games? (Hint: Draw a tree.)

Answer 1

Answer:

The competition can be played in 7 different ways

Step-by-step explanation:

First game : X

Second game : Y

Third game : Y

After that either X or Y can win

¹Case - 1: Y wins the fourth game:

The competition ends with Y winning as he/she won 3 games in a row

Case - 2: X wins the fourth game:

more games are required to decide the winner

Sub-case - a: X wins the fifth game:

more games are required to decide the winner

²Sub-sub-case - i: X wins the sixth game:

The competition ends with X winning as he/she won 3 games in a row

³⁻⁴Sub-sub-case - ii: Y wins the sixth game:

The competition ends after the seventh game. Whoever wins seventh game wins the competition as he/she would've won 4 games in total by then.

Sub-case - b: Y wins the fifth game:

more games are required to decide the winner

⁵Sub-sub-case - i: Y wins the sixth game:

The competition ends with Y winning as he/she won 4 games in total

⁶⁻⁷Sub-sub-case - ii: X wins the sixth game:

The competition ends after the seventh game. Whoever wins seventh game wins the competition as he/she would've won 4 games in total by then.

∴The competition can be played in 7 different ways