# Captive Friends

$$20$$ men are held captive by a pirate lord, including two friends Jack and Tony.

The pirate decides to set $$10$$ of them free. The $$20$$ men are randomly divided into $$10$$ pairs. Each pair of men then flip a fair coin to decide who goes free.

The probability that both Jack and Tony are set free is $$\frac{A}{B}$$ where $$A$$ and $$B$$ are co-prime positive integers. Find the value of $$A+B.$$

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