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The sum of digits of a \(seven\) digit number is \(59\)

Find the probability that this number is divisible by \(11\).

Mayank challenges Akul that he can't do that without invoking the principle of counting. Akul accepts the challenge and to Mayank's surprise, solves it without counting.

Can you figure out how Akul had solved.

If the answer is in the form \(\frac{a}{b}\). Find \(a + b\) where \(a\) and \(b\) don't have a common factor.

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