Number of outcomes possible for best-of-nine series

Hello, oldguynewstudent!

Quote:

How many different outcomes are there in a best-of-nine series
between two teams A and B? Generalize to a best-of-n series where n is odd.

$\text{xxxxA} \quad \text{xxxxxA} \quad \text{xxxxxxA} \quad \text{xxxxxxxA} \quad \text{xxxxxxxxA}$
. ${4\choose4} \;\;+\;\; {5\choose4} \;\;+\;\; {6\choose4} \quad+\quad {7\choose4} \quad+\quad {8\choose4}$ . . = .the number of outcomes where $A$ wins the series.

Multiply this by two to get number of outcomes where $A$ or $B$ wins the series.

$\text{For best-of-}n\text{ where }n\text{ is odd: }\;\;2\cdot\!\!\sum_{k=\frac{n-1}{2}}^{n-1}{k\choose\frac{n-1}{2}}$

Does this look correct? . Yes!

It all looks great! . . . Nice work!