Question 25
The diagram below on the left shows a map, where cities and roads are interconnected, such that there is unique path, between any two cities, without passing any road more than once. Let $x$ be the number of ways to labell the cities by the numbers 1, 2, …, 10 such that every path starting from city $A$ are all strictly increasing. What is the value of $\frac x{20}$? The diagram below on the right shows one example.
