Divisibility by 11 of a 9-digit integer.

Number Theory Level 5

Michelle forms a 9-digit integer by arranging the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 in random order.

What is the probability that this integer is divisible by 11?

If the probability can be expressed as $\dfrac ab$ for co-prime positive integers $a$ and $b$ , find the value of $a+b$ .

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