Question

In a hockey series between team $X$ and $Y$, they decide to play till a team wins '$10$' match. Then the number of ways in which team $X$ wins is $\frac{{}^{20}{C}_m}{2}$, then $m$ equals.

Answer 1

For a team to win the tournament in $k$ matches ,it has to win $9$ matches in $k-1$ matches and then win the $k^{th}$ match

Number of ways is ${}^9{C}_9{+}^{10}{C}_9{+}^{11}{C}_9{+}^{12}{C}_9+....{+}^{18}{C}_9{=}^{19}{C}_{10}=\frac{{}^{20}{C}_{10}}{2}$

$⟹m=10$