Originally Posted by

**Plato** **Actually you are right. There are 42 ways to have 41 wins and 41 losses. **

Lets simplify the question to five wins and five losses, with no consecutive losses.

Look at the string $\displaystyle \underline {\,\,\,\,\,\,} W\underline {\,\,\,\,\,\,} W\underline {\,\,\,\,\,\,} W\underline {\,\,\,\,\,\,} W\underline {\,\,\,\,\,\,} W\underline {\,\,\,\,\,\,} $. Now we have six places to put five $\displaystyle L's$ or $\displaystyle \binom{6}{5}=6$.

I was far to tired to have been working on that last night. Thank you for seeing that that.