Assume that Bob answers all problems with $$\frac{7}{13}$$ probability of being correct. He gets only 10 problems correct, surprisingly in a row, out of the 30 he solves. If the probability that happens is $$\frac{p}{q}$$, where $$p$$ and $$q$$ are coprime positive integers, find the last $$3$$ digits of $$p+q$$.