# Combinatorics combined with Probability

If the integers $$P$$ and $$Q$$ are chosen at random between the numbers 1 and 100 inclusive with repetition, and the probability that with these chosen numbers, the value of $$7^P + 7^Q$$ is divisible by 5 is $$\dfrac AB$$, where $$A$$ and $$B$$ are coprime positive integers.

Find $$5(A+B)+7)$$.

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