Mark and Erik are to play a tennis tournament. The first person to win two games in a row or who wins a total of three games wins the tournament. Find the number of ways the tournament can occur.

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Let $M$ represent that Marck has won a game and $E$ represent Erich has won a game.

Sample space

$S=\{MM, MEMM, MEMEM, MEMEE,$

$MEE,EMM, EMEMM, EMEME,$

$EMEE, EE\}$

It takes no more 5 games to determine a winner.