# Combinatorics combined with Probability

**Discrete Mathematics**Level 4

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 \(5(A+B)+7) \).