is there any way to simplify this expression or write it as a neat, concise formula?
$$ \frac{(2m)!}{2m!} - \frac{(x+y)!}{x!y!} \cdot \frac{ [2m-(x+y)]!}{ (m-x)!(m-y)!} $$
Thank you!
2026-04-02 18:47:15.1775155635
Is there any way to simplify this difference of factorials?
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The neatest possible I guess would be $$ \frac{m!}{2} \cdot \binom{2m}{m} - \binom{x+y}{x} \cdot \binom{2m-(x+y)}{m-x} $$