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Number theory Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

The digits from $1$ to $9$ are randomly arranged to make a $9$ -digit number. What is the probability that the resulting number is divisible by $18$ ?

(A) $\frac{1}{3}$ (B) $\frac{4}{9}$ (C) $\frac{1}{2}$ (D) $\frac{5}{9}$ (E) $\frac{3}{4}$

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Source: UK Mathematics Trust, licensed © UK Mathematics Trust; past papers published free at ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.