If a certain user has exactly 700 followers and a problem of his can be liked only by his followers with a chance of 0.5. Find the probability that his problem will get at least 3 likes.

The probability can be expressed as \(\dfrac{{b}^{c}-a}{{b}^{c}}\) where a and b are coprime positive integers with \(b\) prime.

Give your answer as \(a+b+c\).

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