Competitive Musical Chairs!

You play musical chairs with 28 other people. The game start with 17 chairs.

The probability that you will not reach the final 10 rounds is ${\frac{a}{b}}$ .

What is the value of ${a+b}$ ?

$\textbf{Details and Assumptions}$

In musical chairs, players have to sit down on a chair by the end of the round. If a player isn't able to find a chair to sit down on by the end of the round, they are eliminated from the game. Every round, a chair is removed. The game ends when there is only one chair remaining, and the winner is the player that sits on the final chair. Each player has an equal chance of finding a chair.

The fraction ${\frac{a}{b}}$ is in its simplest form.

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This question is part of the set Musical Chairs . If you liked this question, try some of the other questions as well!