CEMC Fermat, 2003

Combinatorics Difficulty 2.0 Junior Find the answer Canada

In the diagram, it is only possible to travel along an edge in the direction indicated by the arrow. Hazel studied the figure, and determined all the possible routes from $A$ to $B$ . She selected one of these routes at random. What is the probability that she selected a route which passes through $X$ ?

(A) $\frac{8}{11}$ (B) $\frac{3}{11}$ (C) $1$ (D) $\frac{9}{11}$ (E) $\frac{6}{11}$

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