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
<h3>¹Case - 1: Y wins the fourth game:</h3>The competition ends with Y winning as he/she won 3 games in a row
<h3>Case - 2: X wins the fourth game:</h3>more games are required to decide the winner
<h3>Sub-case - a: X wins the fifth game:</h3>more games are required to decide the winner
<h3>²Sub-sub-case - i: X wins the sixth game:</h3>The competition ends with X winning as he/she won 3 games in a row
<h3>³⁻⁴Sub-sub-case - ii: Y wins the sixth game:</h3>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.
<h3>Sub-case - b: Y wins the fifth game:</h3>more games are required to decide the winner
<h3>⁵Sub-sub-case - i: Y wins the sixth game:</h3>The competition ends with Y winning as he/she won 4 games in total
<h3>⁶⁻⁷Sub-sub-case - ii: X wins the sixth game:</h3>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.
∴<u>The competition can be played in 7 different ways</u>
