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 $a+b+c$.