# Number of outcomes possible for best-of-nine series

#### oldguynewstudent

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.
xxxxA xxxxxA xxxxxxA xxxxxxxA xxxxxxxxA
$$\displaystyle \left({4\atop 4}\right)+\left({5\atop 4}\right)+\left({6\atop 4}\right)+\left({7\atop 4}\right)+\left({8\atop 4}\right)=$$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. For best-of-n where n is odd
$$\displaystyle 2*\sum_{k=\frac{n-1}{2}}^{n-1}\left({k\atop \frac{n-1}{2}}\right)$$

Does this look correct?

#### Soroban

MHF Hall of Honor
Hello, oldguynewstudent!

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.

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

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

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

Does this look correct? . Yes!

It all looks great! . . . Nice work!

• oldguynewstudent