# I'll get by with a little help ....

Suppose Silas, Suyeon and Calvin are $$3$$ close friends in a class of $$50$$ students. There is to be a field trip to a local science museum, but the bus can only take $$25$$ students. The (rather devilish) teacher devises an unusual sorting procedure; she randomly divides the $$50$$ students into $$25$$ pairs, and then each pair flips a coin to see which member of the pair gets to go on the field trip.

The probability that the $$3$$ close friends mentioned above all end up going on the field trip is $$\dfrac{a}{b}$$, where $$a$$ and $$b$$ are positive coprime integers. Find $$a + b$$.

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