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The answer is 4/9 or 44.444... % Any permutation of the digits 1 to 9 will be divisible by 9. So divisibility by 18 depends only on whether or not the last digit is even. If the last digit is 2, 4, 6 or 8 the number is divisible by 18 and if it is 1, 3, 5, 7 or 9 it is not. So 4 favourable outcomes out of 9 ie probability = 4/9.

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Q: The digits 1 through 9 are randomly arranged to make a number What is the probability that the resulting number is divisible by 18?
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