#10

There are five cities $A,B,C,D,E$ on a certain island.Each city is connected to every other city by road . In how many ways can a person starting from city $A$ come back to $A$ after visiting a city more than once and without taking the same road more than once? (The order in which he visits the cities also matters e.g the routes $A\rightarrow B \rightarrow C \rightarrow A$ and $A\rightarrow C \rightarrow B \rightarrow A$ are different.

#Combinatorics

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
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Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$